BusyBeaverWiki - User contributions [en]

BB(3,4)

2026-05-11T19:06:39Z

XnoobSpeakable: /* Phase 3 */ fix sigfigs consistancy

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos worked on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: Uses two substages, rather than subtasks, applying Reverse-Engineer and Backtracking deciders.

Stage 10 is also seperated into substages A, B, and C for ease of computation.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,733,388
|13,334,244
|2.91%
|Phase 2 stage 10B
|275
|200 / 75
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,334,244
|12,435,284
|6.74%
|Phase 2 stage 10C
|267
|190 / 77
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>Phase 2 stage 10a:<pre>chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 30000 NG_n 8 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 6 H 1 tH 2 n 8 run</pre>Phase 2 stage 10b:<pre>MitM_CTL CPS_LRU sim 1,001 maxT 10000 LRUH 2 H 0 tH 0 n 20 run
chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 100000 NG_n 4 run</pre>Phase 2 stage 10c:<pre>chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 100000 NG_n 8 run
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 100000 NG_n 11 run</pre></div></div>

== Phase 3 ==

Phase 3 began with Andrew Ducharme applying a FAR decider by mxdys. The following stages were done by XnoobSpeakable. The "Substages" column refers to the amount of separate runs of deciders being applied to the full holdout list, the files are not split into smaller chunks ("Subtasks") like in Phase 2. (Note that Phase 2 stage 9 did actually use substages, like all of Phase 3.)

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Substages
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |Andrew Ducharme
|12,435,284
|12,049,358
|3.10%
| style="text-align:left" |Phase 3 stage 1
|1
|[https://drive.google.com/drive/folders/1lNKc_GF2sa5ZfosleAlMNBQ3uJV4qClo Google Drive]
|No
|-
|XnoobSpeakable
|12,049,358
|11,362,197
|5.70%
|Phase 3 stage 2
|4
|[https://drive.google.com/drive/folders/1lNKc_GF2sa5ZfosleAlMNBQ3uJV4qClo Google Drive]
|No
|}

== Phase 3 Data ==
Here we will list the deciders applied during the various stages of Phase 3. Some stages have a number of TMs solved by every decider at the end of each row.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 2 368,121
FAR CPS_LRU maxT 100000 LRUH 1 H 0 tH 0 n [1-4] 17,660
FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 1 145
</pre>

[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2026-05-11T19:05:39Z

XnoobSpeakable: /* Phase 3 */ stage 2 finally done

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos worked on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: Uses two substages, rather than subtasks, applying Reverse-Engineer and Backtracking deciders.

Stage 10 is also seperated into substages A, B, and C for ease of computation.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,733,388
|13,334,244
|2.91%
|Phase 2 stage 10B
|275
|200 / 75
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,334,244
|12,435,284
|6.74%
|Phase 2 stage 10C
|267
|190 / 77
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>Phase 2 stage 10a:<pre>chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 30000 NG_n 8 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 6 H 1 tH 2 n 8 run</pre>Phase 2 stage 10b:<pre>MitM_CTL CPS_LRU sim 1,001 maxT 10000 LRUH 2 H 0 tH 0 n 20 run
chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 100000 NG_n 4 run</pre>Phase 2 stage 10c:<pre>chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 100000 NG_n 8 run
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 100000 NG_n 11 run</pre></div></div>

== Phase 3 ==

Phase 3 began with Andrew Ducharme applying a FAR decider by mxdys. The following stages were done by XnoobSpeakable. The "Substages" column refers to the amount of separate runs of deciders being applied to the full holdout list, the files are not split into smaller chunks ("Subtasks") like in Phase 2. (Note that Phase 2 stage 9 did actually use substages, like all of Phase 3.)

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Substages
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |Andrew Ducharme
|12,435,284
|12,049,358
|3.10%
| style="text-align:left" |Phase 3 stage 1
|1
|[https://drive.google.com/drive/folders/1lNKc_GF2sa5ZfosleAlMNBQ3uJV4qClo Google Drive]
|No
|-
|XnoobSpeakable
|12,049,358
|11,362,197
|5.7%
|Phase 3 stage 2
|4
|[https://drive.google.com/drive/folders/1lNKc_GF2sa5ZfosleAlMNBQ3uJV4qClo Google Drive]
|No
|}

== Phase 3 Data ==
Here we will list the deciders applied during the various stages of Phase 3. Some stages have a number of TMs solved by every decider at the end of each row.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 2 368,121
FAR CPS_LRU maxT 100000 LRUH 1 H 0 tH 0 n [1-4] 17,660
FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 1 145
</pre>

[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2026-05-11T18:23:00Z

XnoobSpeakable: /* Phase 3 */ bb(3,4) stage 2

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos worked on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: Uses two substages, rather than subtasks, applying Reverse-Engineer and Backtracking deciders.

Stage 10 is also seperated into substages A, B, and C for ease of computation.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,733,388
|13,334,244
|2.91%
|Phase 2 stage 10B
|275
|200 / 75
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,334,244
|12,435,284
|6.74%
|Phase 2 stage 10C
|267
|190 / 77
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>Phase 2 stage 10a:<pre>chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 30000 NG_n 8 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 6 H 1 tH 2 n 8 run</pre>Phase 2 stage 10b:<pre>MitM_CTL CPS_LRU sim 1,001 maxT 10000 LRUH 2 H 0 tH 0 n 20 run
chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 100000 NG_n 4 run</pre>Phase 2 stage 10c:<pre>chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 100000 NG_n 8 run
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 100000 NG_n 11 run</pre></div></div>

== Phase 3 ==

Phase 3 began with Andrew Ducharme applying a FAR decider by mxdys. The following stages were done by XnoobSpeakable. The "Substages" column refers to the amount of separate runs of deciders being applied to the full holdout list, the files are not split into smaller chunks ("Subtasks") like in Phase 2. (Note that Phase 2 stage 9 did actually use substages, like all of Phase 3.)

<nowiki>*</nowiki>Stage 2. The amount of holdouts is unclear due to a minor discrepancy with the predicted and observed counts.

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Substages
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |Andrew Ducharme
|12,435,284
|12,049,358
|3.10%
| style="text-align:left" |Phase 3 stage 1
|1
|[https://drive.google.com/drive/folders/1lNKc_GF2sa5ZfosleAlMNBQ3uJV4qClo Google Drive]
|No
|-
|XnoobSpeakable
|12,049,358
|11,362,200*
|
|Phase 3 stage 2
|4
|[https://drive.google.com/drive/folders/1lNKc_GF2sa5ZfosleAlMNBQ3uJV4qClo Google Drive]
|No
|}

== Phase 3 Data ==
Here we will list the deciders applied during the various stages of Phase 3. Some stages have a number of TMs solved by every decider at the end of each row.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 2 368,121
FAR CPS_LRU maxT 100000 LRUH 1 H 0 tH 0 n [1-4] 17,660
FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 1 145
</pre>

[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2026-05-07T18:46:33Z

XnoobSpeakable: /* Phase 3 */ substage C

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos worked on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: Uses two substages, rather than subtasks, applying Reverse-Engineer and Backtracking deciders.

Stage 10 is also seperated into substages A, B, and C for ease of computation.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,733,388
|13,334,244
|2.91%
|Phase 2 stage 10B
|275
|200 / 75
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,334,244
|12,435,284
|6.74%
|Phase 2 stage 10C
|267
|190 / 77
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>Phase 2 stage 10a:<pre>chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 30000 NG_n 8 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 6 H 1 tH 2 n 8 run</pre>Phase 2 stage 10b:<pre>MitM_CTL CPS_LRU sim 1,001 maxT 10000 LRUH 2 H 0 tH 0 n 20 run
chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 100000 NG_n 4 run</pre>Phase 2 stage 10c:<pre>chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 100000 NG_n 8 run
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 100000 NG_n 11 run</pre></div></div>

== Phase 3 ==

Phase 3 began with Andrew Ducharme applying a FAR decider by mxdys. The following stages were done by XnoobSpeakable. The "Substages" column refers to the amount of separate runs of deciders being applied to the full holdout list, the files are not split into smaller chunks ("Subtasks") like in Phase 2. (Note that Phase 2 stage 9 did actually use substages, like all of Phase 3.)

Stage 2 is currently in progress, with 2 substages completed. The amount of holdouts is unclear due to a minor discrepancy with the predicted and observed counts.

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Substages
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |Andrew Ducharme
|12,435,284
|12,049,358
|3.10%
| style="text-align:left" |Phase 3 stage 1
|1
|[https://drive.google.com/drive/folders/1lNKc_GF2sa5ZfosleAlMNBQ3uJV4qClo Google Drive]
|No
|-
|XnoobSpeakable
|12,049,358
|≤11,368,507
|
|Phase 3 stage 2
|3/4 (in prog.)
|[https://drive.google.com/drive/folders/1lNKc_GF2sa5ZfosleAlMNBQ3uJV4qClo Google Drive]
|No
|}

== Phase 3 Data ==
Here we will list the deciders applied during the various stages of Phase 3. Some stages have a number of TMs solved by every decider at the end of each row.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 2 368,121
FAR CPS_LRU maxT 100000 LRUH 1 H 0 tH 0 n [1-4] 17,660
FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 1 145
</pre>

[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2026-05-05T11:35:47Z

XnoobSpeakable: /* Phase 3 */ update holdouts

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos worked on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: Uses two substages, rather than subtasks, applying Reverse-Engineer and Backtracking deciders.

Stage 10 is also seperated into substages A, B, and C for ease of computation.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,733,388
|13,334,244
|2.91%
|Phase 2 stage 10B
|275
|200 / 75
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,334,244
|12,435,284
|6.74%
|Phase 2 stage 10C
|267
|190 / 77
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>Phase 2 stage 10a:<pre>chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 30000 NG_n 8 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 6 H 1 tH 2 n 8 run</pre>Phase 2 stage 10b:<pre>MitM_CTL CPS_LRU sim 1,001 maxT 10000 LRUH 2 H 0 tH 0 n 20 run
chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 100000 NG_n 4 run</pre>Phase 2 stage 10c:<pre>chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 100000 NG_n 8 run
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 100000 NG_n 11 run</pre></div></div>

== Phase 3 ==

Phase 3 began with Andrew Ducharme applying a FAR decider by mxdys. The following stages were done by XnoobSpeakable. The "Substages" column refers to the amount of separate runs of deciders being applied to the full holdout list, the files are not split into smaller chunks ("Subtasks") like in Phase 2. (Note that Phase 2 stage 9 did actually use substages, like all of Phase 3.)

Stage 2 is currently in progress, with 2 substages completed. The amount of holdouts is unclear due to a minor discrepancy with the predicted and observed counts.

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Substages
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |Andrew Ducharme
|12,435,284
|12,049,358
|3.10%
| style="text-align:left" |Phase 3 stage 1
|1
|[https://drive.google.com/drive/folders/1lNKc_GF2sa5ZfosleAlMNBQ3uJV4qClo Google Drive]
|No
|-
|XnoobSpeakable
|12,049,358
|≤11,852,797
|
|Phase 3 stage 2
|2/4 (in prog.)
|[https://drive.google.com/drive/folders/1lNKc_GF2sa5ZfosleAlMNBQ3uJV4qClo Google Drive]
|No
|}

== Phase 3 Data ==
Here we will list the deciders applied during the various stages of Phase 3. Some stages have a number of TMs solved by every decider at the end of each row.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 2 368,121
FAR CPS_LRU maxT 100000 LRUH 1 H 0 tH 0 n [1-4] 17,660
FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 1 145
</pre>

[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2026-05-04T16:42:29Z

XnoobSpeakable: /* Phase 3 */ Fixed explanation issue

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos worked on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: Uses two substages, rather than subtasks, applying Reverse-Engineer and Backtracking deciders.

Stage 10 is also seperated into substages A, B, and C for ease of computation.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,733,388
|13,334,244
|2.91%
|Phase 2 stage 10B
|275
|200 / 75
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,334,244
|12,435,284
|6.74%
|Phase 2 stage 10C
|267
|190 / 77
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>Phase 2 stage 10a:<pre>chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 30000 NG_n 8 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 6 H 1 tH 2 n 8 run</pre>Phase 2 stage 10b:<pre>MitM_CTL CPS_LRU sim 1,001 maxT 10000 LRUH 2 H 0 tH 0 n 20 run
chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 100000 NG_n 4 run</pre>Phase 2 stage 10c:<pre>chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 100000 NG_n 8 run
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 100000 NG_n 11 run</pre></div></div>

== Phase 3 ==

Phase 3 began with Andrew Ducharme applying a FAR decider by mxdys. The following stages were done by XnoobSpeakable. The "Substages" column refers to the amount of separate runs of deciders being applied to the full holdout list, the files are not split into smaller chunks ("Subtasks") like in Phase 2. (Note that Phase 2 stage 9 did actually use substages, like all of Phase 3.)

Stage 2 is currently in progress, with 2 substages completed. The amount of holdouts is unclear due to a minor discrepancy with the predicted and observed counts.

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Substages
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |Andrew Ducharme
|12,435,284
|12,049,358
|3.10%
| style="text-align:left" |Phase 3 stage 1
|1
|[https://drive.google.com/drive/folders/1lNKc_GF2sa5ZfosleAlMNBQ3uJV4qClo Google Drive]
|No
|-
|XnoobSpeakable
|12,049,358
|≤11,894,437
|
|Phase 3 stage 2
|2/4 (in prog.)
|[https://drive.google.com/drive/folders/1lNKc_GF2sa5ZfosleAlMNBQ3uJV4qClo Google Drive]
|No
|}

== Phase 3 Data ==
Here we will list the deciders applied during the various stages of Phase 3. Some stages have a number of TMs solved by every decider at the end of each row.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 2 368,121
FAR CPS_LRU maxT 100000 LRUH 1 H 0 tH 0 n [1-4] 17,660
FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 1 145
</pre>

[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2026-05-04T16:41:47Z

XnoobSpeakable: /* Phase 3 */ A lot of stage and substage stuff

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos worked on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: Uses two substages, rather than subtasks, applying Reverse-Engineer and Backtracking deciders.

Stage 10 is also seperated into substages A, B, and C for ease of computation.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,733,388
|13,334,244
|2.91%
|Phase 2 stage 10B
|275
|200 / 75
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,334,244
|12,435,284
|6.74%
|Phase 2 stage 10C
|267
|190 / 77
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>Phase 2 stage 10a:<pre>chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 30000 NG_n 8 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 6 H 1 tH 2 n 8 run</pre>Phase 2 stage 10b:<pre>MitM_CTL CPS_LRU sim 1,001 maxT 10000 LRUH 2 H 0 tH 0 n 20 run
chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 100000 NG_n 4 run</pre>Phase 2 stage 10c:<pre>chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 100000 NG_n 8 run
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 100000 NG_n 11 run</pre></div></div>

== Phase 3 ==

Phase 3 began with Andrew Ducharme applying a FAR decider by mxdys. The following stages were done by XnoobSpeakable. The "Substages" column refers to the amount of separate runs of deciders were applied to the full holdout list, the files are not split into smaller chunks ("Substages") like in Phase 2. (Note that Phase 2 stage 9 did actually use substages, like all of Phase 3.)

Stage 2 is currently in progress, with 2 substages completed. The amount of holdouts is unclear due to a minor discrepancy with the predicted and observed counts.

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Substages
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |Andrew Ducharme
|12,435,284
|12,049,358
|3.10%
| style="text-align:left" |Phase 3 stage 1
|1
|[https://drive.google.com/drive/folders/1lNKc_GF2sa5ZfosleAlMNBQ3uJV4qClo Google Drive]
|No
|-
|XnoobSpeakable
|12,049,358
|≤11,894,437
|
|Phase 3 stage 2
|2/4 (in prog.)
|[https://drive.google.com/drive/folders/1lNKc_GF2sa5ZfosleAlMNBQ3uJV4qClo Google Drive]
|No
|}

== Phase 3 Data ==
Here we will list the deciders applied during the various stages of Phase 3. Some stages have a number of TMs solved by every decider at the end of each row.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 2 368,121
FAR CPS_LRU maxT 100000 LRUH 1 H 0 tH 0 n [1-4] 17,660
FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 1 145
</pre>

[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2026-05-03T12:54:20Z

XnoobSpeakable: /* Phase 3 */ Working on phase 3 table and stages

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos worked on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: The two subtasks are seperate sub-stages, applying Reverse-Engineer and Backtracking deciders.

Stage 10 is also seperated into substages A, B, and C for ease of computation.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,733,388
|13,334,244
|2.91%
|Phase 2 stage 10B
|275
|200 / 75
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,334,244
|12,435,284
|6.74%
|Phase 2 stage 10C
|267
|190 / 77
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>Phase 2 stage 10a:<pre>chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 30000 NG_n 8 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 6 H 1 tH 2 n 8 run</pre>Phase 2 stage 10b:<pre>MitM_CTL CPS_LRU sim 1,001 maxT 10000 LRUH 2 H 0 tH 0 n 20 run
chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 100000 NG_n 4 run</pre>Phase 2 stage 10c:<pre>chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 100000 NG_n 8 run
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 100000 NG_n 11 run</pre></div></div>

== Phase 3 ==

Phase 3 began with Andrew Ducharme applying a FAR decider by mxdys. The "Subtasks" column refers to how many portions the holdouts list was split into during computation.

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |Andrew Ducharme
|12,435,284
|12,049,358
|3.10%
| style="text-align:left" |Phase 3 stage 1
|1
|[https://drive.google.com/drive/folders/1lNKc_GF2sa5ZfosleAlMNBQ3uJV4qClo Google Drive]
|No
|-
|XnoobSpeakable
|12,049,358
|(TBD)
|
|Phase 3 stage 2
|241
|
|
|}

== Phase 3 Data ==
Here we will list the deciders applied during the various stages of Phase 3. Some stages have a number of TMs solved by every decider at the end of each row.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 2 368,121
FAR CPS_LRU maxT 100000 LRUH 1 H 0 tH 0 n [1-4] 17,660
FAR CPS_LRU maxT 100000 LRUH 2 H 0 tH 0 n 1 145
</pre>

[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2026-01-01T09:52:03Z

XnoobSpeakable: /* Phase 2 Data */ fix typo

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: The two subtasks are seperate sub-stages, applying Reverse-Engineer and Backtracking deciders.

Stage 10 is also seperated into substages A, B, and C for ease of computation.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,733,388
|13,334,244
|2.91%
|Phase 2 stage 10B
|275
|200 / 75
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,334,244
|12,435,284
|6.74%
|Phase 2 stage 10C
|267
|190 / 77
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>Phase 2 stage 10a:<pre>chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 30000 NG_n 8 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 6 H 1 tH 2 n 8 run</pre>Phase 2 stage 10b:<pre>MitM_CTL CPS_LRU sim 1,001 maxT 10000 LRUH 2 H 0 tH 0 n 20 run
chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 100000 NG_n 4 run</pre>Phase 2 stage 10c:<pre>chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 100000 NG_n 8 run
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 100000 NG_n 11 run</pre></div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-12-31T15:07:57Z

XnoobSpeakable: /* Phase 2 Data */ attempt formatting fix

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: The two subtasks are seperate sub-stages, applying Reverse-Engineer and Backtracking deciders.

Stage 10 is also seperated into substages A, B, and C for ease of computation.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,733,388
|13,334,244
|2.91%
|Phase 2 stage 10B
|275
|200 / 75
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,334,244
|12,435,284
|6.74%
|Phase 2 stage 10C
|267
|190 / 77
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>Phase 2 stage 10a:<pre>chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 30000 NG_n 8 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 6 H 1 tH 2 n 8 run</pre>Phase 2 stage 10b:<pre>MitM_CTL CPS_LRU sim 1,001 maxT 10000 LRUH 2 H 0 tH 0 n 20 run
chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 100000 NG_n 4 run</pre>Phase 2 stage 10b:<pre>chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 100000 NG_n 8 run
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 100000 NG_n 11 run</pre></div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-12-31T15:05:43Z

XnoobSpeakable: /* Phase 2 */ Stage 10C

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: The two subtasks are seperate sub-stages, applying Reverse-Engineer and Backtracking deciders.

Stage 10 is also seperated into substages A, B, and C for ease of computation.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,733,388
|13,334,244
|2.91%
|Phase 2 stage 10B
|275
|200 / 75
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,334,244
|12,435,284
|6.74%
|Phase 2 stage 10C
|267
|190 / 77
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>Phase 2 stage 10a:<pre>chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 30000 NG_n 8 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 6 H 1 tH 2 n 8 run</pre>Phase 2 stage 10b:<pre>MitM_CTL CPS_LRU sim 1,001 maxT 10000 LRUH 2 H 0 tH 0 n 20 run
chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 100000 NG_n 4 run</pre>Phase 2 stage 10c:
</div><pre>chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 100000 NG_n 8 run
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 100000 NG_n 11 run</pre></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-12-24T18:13:43Z

XnoobSpeakable: /* Phase 2 Data */ attempt fix

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: The two subtasks are seperate sub-stages, applying Reverse-Engineer and Backtracking deciders.

Stage 10 is also seperated into substages A, B, and C for ease of computation.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,733,388
|13,334,244
|2.91%
|Phase 2 stage 10B
|275
|200 / 75
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>Phase 2 stage 10a:<pre>chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 30000 NG_n 8 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 6 H 1 tH 2 n 8 run</pre>Phase 2 stage 10b:<pre>MitM_CTL CPS_LRU sim 1,001 maxT 10000 LRUH 2 H 0 tH 0 n 20 run
chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 100000 NG_n 4 run</pre></div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-12-24T18:13:07Z

XnoobSpeakable: /* Phase 2 Data */ test

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: The two subtasks are seperate sub-stages, applying Reverse-Engineer and Backtracking deciders.

Stage 10 is also seperated into substages A, B, and C for ease of computation.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,733,388
|13,334,244
|2.91%
|Phase 2 stage 10B
|275
|200 / 75
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>Phase 2 stage 10a:<pre>
chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 30000 NG_n 8 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 6 H 1 tH 2 n 8 run
</pre>Phase 2 stage 10b:<pre>MitM_CTL CPS_LRU sim 1,001 maxT 10000 LRUH 2 H 0 tH 0 n 20 run
chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 100000 NG_n 4 run</pre></div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-12-24T17:54:25Z

XnoobSpeakable: /* Phase 2 */ fix 10b

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: The two subtasks are seperate sub-stages, applying Reverse-Engineer and Backtracking deciders.

Stage 10 is also seperated into substages A, B, and C for ease of computation.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|13,733,388
|13,334,244
|2.91%
|Phase 2 stage 10B
|275
|200 / 75
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>Phase 2 stage 10a:<pre>
chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 30000 NG_n 8 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 6 H 1 tH 2 n 8 run
</pre>Phase 2 stage 10b:<pre>
MitM_CTL CPS_LRU sim 1,001 maxT 10000 LRUH 2 H 0 tH 0 n 20 run
chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 100000 NG_n 4 run
</pre></div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-12-24T17:53:57Z

XnoobSpeakable: /* Phase 2 */ stage 10b + fixes in 10a data

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: The two subtasks are seperate sub-stages, applying Reverse-Engineer and Backtracking deciders.

Stage 10 is also seperated into substages A, B, and C for ease of computation.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10B
|275
|200 / 75
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>Phase 2 stage 10a:<pre>
chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 30000 NG_n 8 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 6 H 1 tH 2 n 8 run
</pre>Phase 2 stage 10b:<pre>
MitM_CTL CPS_LRU sim 1,001 maxT 10000 LRUH 2 H 0 tH 0 n 20 run
chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 100000 NG_n 4 run
</pre></div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-12-22T14:51:24Z

XnoobSpeakable: /* Phase 2 Data */ data

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: The two subtasks are seperate sub-stages, applying Reverse-Engineer and Backtracking deciders.

Stage 10 is also seperated into substages A, B, and C for ease of computation.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>Phase 2 stage 10a:<pre>
chr_LRUH 28 chr_LRUn 2 MitM_CTL NG maxT 30,000 NG_n 8 run
MitM_CTL CPS_LRU sim 1,001 maxT 10,000 LRUH 6 H 1 tH 2 n 8 run
</pre></div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-12-22T14:50:07Z

XnoobSpeakable: /* Phase 2 Data */ info

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: The two subtasks are seperate sub-stages, applying Reverse-Engineer and Backtracking deciders.

Stage 10 is also seperated into substages A, B, and C for ease of computation.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>
</div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-12-22T14:46:43Z

XnoobSpeakable: /* Phase 2 */ Stage 10A

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: The two subtasks are seperate sub-stages, applying Reverse-Engineer and Backtracking deciders.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|14,413,460
|13,733,388
|4.72%
|Phase 2 stage 10A
|289
|216 / 73
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>
</div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-12-18T10:53:04Z

XnoobSpeakable: /* Phase 2 */ Stage 9

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>**</nowiki>Stage 9: The two subtasks are seperate sub-stages, applying Reverse-Engineer and Backtracking deciders.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|14,518,243
|14,413,460
|0.72%
|Phase 2 stage 9
|2**
|2 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>Phase 2 stage 9a:<pre>python3 Code/Reverse_Engineer_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst8/3x4_holdouts_14518243.txt' --outfile='out.txt'</pre>Phase 2 stage 9b:<pre>python3 ./Code/Backtracking_Filter.py --infile='/home/xnoobspeakable/Desktop/Busy Beavers/BB(3,4)/resultsst9/unknown.txt' --outfile='./b1.pb' --steps=100</pre>
</div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

Holdouts lists

2025-12-13T18:36:32Z

XnoobSpeakable: BB(3,4)

A '''holdout''' (or undecided machine) is a [[Turing machine]] for which it is not known whether the machine halts or not from all-0 input tape. Holdouts are the machines which [[Decider|deciders]] are yet unable to decide.

Holdout lists are often shared by contributors. There is a [[#Downloadable Holdout Lists|Downloadable Holdout Lists]] table where people have added lists with no restriction or independent verification. For some of the entries there is a reference to a spreadsheet that documents what was run to achieve the result. For others, there is additional documentation on the specific BB pages. They may exclude known equivalent machines, whose halting status is implied by the halting status of another machine.

The table with the "Number of holdouts" is based on the holdout lists listed in the table below it. Thus, some of these numbers have not been independently verified. All the zero entries (no remaining holdouts) have been verified.

{| class="wikitable"
|+Number of holdouts
!
!2-state
!3-state
!4-state
!5-state
!6-state
!7-state
|-
!2-symbol
|0
|0
|0
|0
|1,416
|20,405,295
|-
!3-symbol
|0
|6
|9,401,447
|
|
|
|-
!4-symbol
|0
|14,518,243
|
|
|
|
|-
!5-symbol
|75
|
|
|
|
|
|-
!6-symbol
|870,085
|
|
|
|
|
|}

== Downloadable Holdout Lists ==
{| class="wikitable sortable"
|+
!BB space
!Date
!Shared by
!Number of holdouts
!File
!Notes
|-
|[[BB(6)]]
|November 28th, 2025
|@mxdys
|1416
|[https://wiki.bbchallenge.org/w/images/9/98/BB6_holdouts_1416.txt BB6_holdouts_1416.txt]
|
|-
|[[BB(6)]]
|November 22nd, 2025
|Robin Rovenszky
|~1534
|[https://docs.google.com/spreadsheets/d/10y2aMp9yZVLyN-nXAxgA25rw4EA_lJqn3Vxy2kB-m-U/edit?gid=1330361301#gid=1330361301 Google Sheets]
|Annotated list, including links to Discord discussions
|-
|[[BB(6)]]
|November 14th, 2025
|@mxdys
|1534
|[https://wiki.bbchallenge.org/w/images/0/02/BB6_holdouts_1534.txt BB6_holdouts_1534.txt]
|
|-
|[[BB(6)]]
|October 20th, 2025
|@mxdys
|1618
|[https://wiki.bbchallenge.org/w/images/e/e3/BB6_holdouts_1618.txt BB6 holdouts 1618.txt]
|
|-
|[[BB(3,4)]]
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i October 4th, 2025]
|@tjligocki
|64,777,377
|[https://drive.google.com/file/d/1I3s3w-T4NPLn-eCdaZLPgC2Mya51pyvH/view?usp=drive_link 3x4_holdouts_64777377.txt.gz]
|Work done by [[User:XnoobSpeakable|XnoobSpeakable]] and [[User:WarpedWartWars|Lúkos]].
|-
|[[BB(7)]]
|[https://discord.com/channels/960643023006490684/1369339127652159509/1423806362072256676 October 4th, 2025]
|Andrew Ducharme
|22,721,168
|[https://drive.google.com/file/d/1xAFSPh6qAR8VxsF4QVipmdc0UpdPC1hn/view bb7_holdouts_22721168.txt.zip]
|
|-
|[[BB(2,6)]]
|[https://drive.google.com/drive/folders/1TsSpW27x3LBlu5qmk-cjzCJzgo_3ehyT September 22nd, 2025]
|@tjligocki
|873,469
|[http://2x6_holdouts_873469.txt.zip 2x6_holdouts_873469.txt.zip]
|Work done by Andrew Ducharme.
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1411308408220549140 August 30 2025]
|@mxdys
|2,592
|[[:File:BB6 holdouts 2592.txt|BB6 holdouts 2592.txt]]
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1399783936019664896 July 29 2025]
|@mxdys
|2,728
|[[:File:BB6 holdouts 2728.txt|BB6 holdouts 2728.txt]]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1259770421046411285/1355593937531961365 March 29 2025]
|@mxdys
|83
|[[:File:BB2x5 Coq holdouts 83.txt]]
|
|-
|[[BB(4,3)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1320172124509311004 December 21, 2024]
|@tjligocki
|460,916,384
|[https://drive.google.com/file/d/1hKy0TuPuI62rN95j6ZLjXgE-Pue8tRsK/view?usp=drive_link 4x3_holdouts_460916384.txt.gz]
|[https://drive.google.com/drive/folders/1HBPZ17llVE_8wCy5FvRUFQ5MJsaYXAW-?usp=drive_link Google Drive directory for 4x3 TMs]
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1310648046576730124 November 25, 2024 (@icy)]
|@tjligocki
|4,319
|[https://docs.google.com/spreadsheets/d/1grhW_0neb2I8TfceN5-v70_3W42Z2U159r9L6FhPGf8/edit?usp=sharing Spreadsheet of holdouts]
|Keeping track of BB(6) progress - informal.
|-
|[[BB(3,3)]]
|November 10, 2024
|
|6
|[[:File:3x3 holdout 6.txt|3x3 holdout 6.txt]]
|
|-
|[[BB(6)]]
|[https://discordapp.com/channels/960643023006490684/1239205785913790465/1304303803213942846 November 8, 2024]
|@mxdys
|4,408
|[[:File:BB6 holdouts 4408.txt|BB6_holdouts_4408.txt]]
|
|-
|[[BB(2,6)]]
|[https://discord.com/channels/960643023006490684/960643023530762341/1303219184221683733 November 4, 2024]
|@tjligocki
|22,302,296
|[https://drive.google.com/file/d/1xRLIjdiqImFP2SL38gvhxVlAaX0L1cYO/view?usp=drive_link 2x6_holdouts_22302296.txt.gz]
|[https://drive.google.com/drive/folders/1p9b5g-Id3WEMUYIwEnaKWRBGIW66ADjM?usp=drive_link Google Drive directory for 2x6 TMs]
|-
|[[BB(3,4)]]
|[https://discord.com/channels/960643023006490684/960643023530762341/1302767449476694188 November 3, 2024]
|@tjligocki
|434,787,751
|[https://drive.google.com/file/d/1PLzN3wLw-MRgk1OFmYh4RTwNc30nflR7/view?usp=drive_link 3x4_holdouts_434787751.txt.gz]
|[https://drive.google.com/drive/folders/1bZxl7jg5q9IVvHQNZwItx1kPusAWznZk?usp=drive_link Google Drive directory for 3x4 TMs]
|-
|[[BB(6)]]
|[https://discordapp.com/channels/960643023006490684/1239205785913790465/1280185195877634098 September 2, 2024]
|@mxdys
|5394
|[[:File:BB6 holdouts 5394.txt]]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1269612923127599164 August 4, 2024]
|@mxdys
|5877
|[[:File:BB6 holdouts 5877.txt]]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1259131753176498216 July 6, 2024]
|@mxdys
|7296
|[[:File:BB6 holdouts 7296.txt]]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1252989316175499284 June 19, 2024]
|@mxdys
|217
|[[:File:2x5_holdouts_217.txt]]
|273 holdouts minus machines solved by CTL
|-
|[[BB(2,5)]]
|June 15th 2024
|@dyuan01
| 273
|[[:File:2x5_holdouts_273.txt]]
|@Justin Blanchard's 499 holdouts minus machines solved by @mxdys
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1250895665719148595 June 13, 2024]
|@tjligocki
| 12,091
|[[:File:BB6 holdouts 12091.txt]]
|Work done with @Shawn Ligocki
|-
|[[BB(3,3)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1249142547217907772 June 9, 2024]
|@Justin Blanchard
|22
|[[:File:3x3.todo.txt]], [[:File:Mugshots small.pdf]]
|
|-
|BB(6)
|[https://discord.com/channels/960643023006490684/1239205785913790465/1248708916381220954 June 7, 2024]
|@mxdys
|12,325
|[[:File:BB6 holdouts 12325.txt]]
|Some equivalent machines are removed.
|-
|[[BB(5)]]
|June 2024
|BBChallenge
|0
|
|'''BB(5) is SOLVED!'''
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1242679236142170203 May 22, 2024]
|@Justin Blanchard
|499
|[[:File:2x5.todo.txt]]
|
|-
|[[BB(3,3)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1116351783040716830 June 8, 2023]
|@Iijil
|925
|[[:File:2023 06 08.3x3.holdouts intersect sligocki iijil 925.txt]]
|Intersection of @sligocki and @Iijil from below
|-
|[[BB(3,3)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1116351783040716830 June 8, 2023]
|@Iijil
|2,480
|[[:File:2023 06 08.3x3.holdouts iijil 2380.txt]]
|
|-
|[[BB(3,3)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1116178334620070000 June 7, 2023]
|@sligocki
|2,417
|[[:File:2023 06 07.3x3.holdouts 2417.txt]]
|
|-
|[[BB(6)]]
|May 27, 2023
|@sligocki
|181,851
|[https://drive.google.com/file/d/1YNwFCN6XJeDNKxxK5KbGHOAFOdIBvDb6/view?usp=drive_link 6x2.holdouts_181851.txt.gz]
|This was posted to the BBChallenge Forum (before Discord)
|-
|[[BB(6)]]
|May 10, 2023
|@sligocki
|1,458,704
|[https://drive.google.com/file/d/14bDnBt0OwuHATFBiubc_5jub0220EyXf/view?usp=drive_link 6x2.holdouts_1458704.txt.gz]
|This was posted to the BBChallenge Forum (before Discord)
|-
|[[BB(5)]]
|[https://skelet.ludost.net/bb/nreg.html circa May 13th, 2003]
|Georgi Georgiev (Skelet)
|43
|[https://bbchallenge.org/skelet List of 43 holdouts]
|
|}

BB(3,4)

2025-12-13T13:45:38Z

XnoobSpeakable: /* Phase 2 */ link scripts

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

[https://drive.google.com/drive/folders/1MamU8zivuqoe4j82vpb-jYBfc4wvXNRc All scripts used are available here.] The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>
</div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-12-13T13:44:12Z

XnoobSpeakable: /* Phase 2 */ Stage 8

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stages 3 and 8 are lr_enum_continue computations to 1 million and 10 million steps respectively. Lúkos did not contribute to computing these stages, but rather created a Python script to compute them in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|14,518,243
|4.08%
|Phase 2 stage 8
|303
|303 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 1000000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>Phase 2 stage 8 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 10 million steps):<pre>lr_enum_continue ./in.txt 10000000 ./halt.txt ./inf.txt ./unknown.txt "" false</pre>
</div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-12-10T18:48:56Z

XnoobSpeakable: /* Phase 2 */ progr.

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stage 3 is a lr_enum_continue computation to 1 million steps. Lúkos did not contribute to computing stage 3, but rather created a Python script to compute it in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>*</nowiki>Stage 8 is currently in progress. It is a lr_enum_continue computation to 10 million steps.

The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|'''---'''
|'''---'''
|Phase 2 stage 8
|303
|270* / 0
|'''---'''
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 100000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>
</div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-12-09T19:35:24Z

XnoobSpeakable: /* Phase 2 */ progr.

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stage 3 is a lr_enum_continue computation to 1 million steps. Lúkos did not contribute to computing stage 3, but rather created a Python script to compute it in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>*</nowiki>Stage 8 is currently in progress. It is a lr_enum_continue computation to 10 million steps.

The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|'''---'''
|'''---'''
|Phase 2 stage 8
|303
|226* / 0
|'''---'''
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 100000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>
</div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-12-08T19:39:21Z

XnoobSpeakable: progr.

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stage 3 is a lr_enum_continue computation to 1 million steps. Lúkos did not contribute to computing stage 3, but rather created a Python script to compute it in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>*</nowiki>Stage 8 is currently in progress. It is a lr_enum_continue computation to 10 million steps.

The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|'''---'''
|'''---'''
|Phase 2 stage 8
|303
|205* / 0
|'''---'''
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 100000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>
</div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-12-07T19:01:56Z

XnoobSpeakable: /* Phase 2 */ update progress

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stage 3 is a lr_enum_continue computation to 1 million steps. Lúkos did not contribute to computing stage 3, but rather created a Python script to compute it in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>*</nowiki>Stage 8 is currently in progress. It is a lr_enum_continue computation to 10 million steps.

The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|'''---'''
|'''---'''
|Phase 2 stage 8
|303
|194* / 0
|'''---'''
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 100000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>
</div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-12-07T13:48:56Z

XnoobSpeakable: /* Phase 2 */ Added verified column to keep track of validation

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stage 3 is a lr_enum_continue computation to 1 million steps. Lúkos did not contribute to computing stage 3, but rather created a Python script to compute it in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>*</nowiki>Stage 8 is currently in progress. It is a lr_enum_continue computation to 10 million steps.

The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
! rowspan="2" |Verified
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|Yes
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|No
|-
|XnoobSpeakable
|15,136,283
|'''---'''
|'''---'''
|Phase 2 stage 8
|303
|183* / 0
|'''---'''
|No
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 100000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>
</div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-12-07T13:44:05Z

XnoobSpeakable: /* Phase 2 */ Add stage 8

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stage 3 is a lr_enum_continue computation to 1 million steps. Lúkos did not contribute to computing stage 3, but rather created a Python script to compute it in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

<nowiki>*</nowiki>Stage 8 is currently in progress. It is a lr_enum_continue computation to 10 million steps.

The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable
|15,136,283
|'''---'''
|'''---'''
|Phase 2 stage 8
|303
|183* / 0
|'''---'''
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 100000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>
</div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

List of Busy Beaver Papers

2025-12-04T17:40:43Z

XnoobSpeakable: lynn 1972

{| class="wikitable"
|+
!Title
!Author
!Published
!DOI
!Download
|-
|On Non-Computable Functions
|Tibor Radó
|May 1962
|{{doi|10.1002/j.1538-7305.1962.tb00480.x}}
|
|-
|On a simple source for non-computable functions
|Tibor Radó
|1963
|
|[https://docs.bbchallenge.org/papers/Rado1963.pdf PDF]
|-
|A Lower Bound on Rado's Sigma-Function for Binary Turing Machines
|Milton W. Green
|11-13 November 1964
|{{doi|10.1109/SWCT.1964.3}}
|
|-
|Computer Studies of Turing Machine Problems
|[[Shen Lin]]
Tibor Radó
|1 April 1965
|{{doi|10.1145/321264.321270}}
|
|-
|Solutions of restricted cases of the halting problem applied to the determination of particular values of a non-computable function
|Allen H. Brady
|June 1965
|
|[http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/zk51vk21c Thesis Archive]
|-
|The Conjectured Highest Scoring Machines for Rado's Σ(k) for the Value k = 4
|Allen H. Brady
|31 October 1966
|{{doi|10.1109/PGEC.1966.264572}}
|
|-
|New results for Rado's sigma function for binary Turing machines
|Donald S. Lynn
|31 August 1972
|{{doi|10.1109/TC.1972.5009047}}
|[https://docs.bbchallenge.org/papers/Lynn1972.pdf PDF]
|-
|The solution to Rado's busy beaver game is now decided for k = 4. Preliminary report. (Abstract)
|Allen H. Brady
|January 1975
|
|[https://www.ams.org/journals/notices/197501/197501FullIssue.pdf PDF] (A-25, PDF Page 109)
|}

List of Busy Beaver Papers

2025-12-04T16:14:14Z

XnoobSpeakable: Add paper, change other date

{| class="wikitable"
|+
!Title
!Author
!Published
!DOI
!Download
|-
|On Non-Computable Functions
|Tibor Radó
|May 1962
|{{doi|10.1002/j.1538-7305.1962.tb00480.x}}
|
|-
|On a simple source for non-computable functions
|Tibor Radó
|1963
|
|[https://docs.bbchallenge.org/papers/Rado1963.pdf PDF]
|-
|A Lower Bound on Rado's Sigma-Function for Binary Turing Machines
|Milton W. Green
|11-13 November 1964
|{{doi|10.1109/SWCT.1964.3}}
|
|-
|Computer Studies of Turing Machine Problems
|Shen Lin
Tibor Radó
|1 April 1965
|{{doi|10.1145/321264.321270}}
|
|-
|Solutions of restricted cases of the halting problem applied to the determination of particular values of a non-computable function
|Allen H. Brady
|June 1965
|
|[http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/zk51vk21c Thesis Archive]
|-
|The Conjectured Highest Scoring Machines for Rado's Σ(k) for the Value k = 4
|Allen H. Brady
|31 October 1966
|{{doi|10.1109/PGEC.1966.264572}}
|
|-
|The solution to Rado's busy beaver game is now decided for k = 4. Preliminary report. (Abstract)
|Allen H. Brady
|January 1975
|
|[https://www.ams.org/journals/notices/197501/197501FullIssue.pdf PDF] (A-25, PDF Page 109)
|}

List of Busy Beaver Papers

2025-12-04T15:15:10Z

XnoobSpeakable: Green's paper actual title

{| class="wikitable"
|+
!Title
!Author
!Published
!DOI
!Download
|-
|On Non-Computable Functions
|T. Rado
|May 1962
|10.1002/j.1538-7305.1962.tb00480.x
|
|-
|On a simple source for non-computable functions
|T. Rado
|1963
|
|https://docs.bbchallenge.org/papers/Rado1963.pdf
|-
|A Lower Bound on Rado's Sigma-Function for Binary Turing Machines
|Milton W. Green
|1964 November 11-13
|10.1109/SWCT.1964.3
|
|-
|Solutions of restricted cases of the halting problem applied to the determination of particular values of a non-computable function
|Allen H. Brady
|10 December 1964
|
|http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/zk51vk21c
|-
|The Conjectured Highest Scoring Machines for Rado's Σ(k) for the Value k = 4
|Allen H. Brady
|31 October 1966
|10.1109/PGEC.1966.264572
|
|-
|The solution to Rado's busy beaver game is now decided for k = 4. Preliminary report. (Abstract)
|Allen H. Brady
|January 1975
|
|https://www.ams.org/journals/notices/197501/197501FullIssue.pdf<nowiki/>*
|}*A-25, PDF Page 109.

List of Busy Beaver Papers

2025-12-04T15:11:35Z

XnoobSpeakable: formatting

{| class="wikitable"
|+
!Title
!Author
!Published
!DOI
!Download
|-
|On Non-Computable Functions
|T. Rado
|May 1962
|10.1002/j.1538-7305.1962.tb00480.x
|
|-
|On a simple source for non-computable functions
|T. Rado
|1963
|
|https://docs.bbchallenge.org/papers/Rado1963.pdf
|-
|A lower bound RADO's sigma function for binary turing machines
|Milton W. Green
|1964 November 11-13
|10.1109/SWCT.1964.3
|
|-
|Solutions of restricted cases of the halting problem applied to the determination of particular values of a non-computable function
|Allen H. Brady
|10 December 1964
|
|http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/zk51vk21c
|-
|The Conjectured Highest Scoring Machines for Rado's Σ(k) for the Value k = 4
|Allen H. Brady
|31 October 1966
|10.1109/PGEC.1966.264572
|
|-
|The solution to Rado's busy beaver game is now decided for k = 4. Preliminary report. (Abstract)
|Allen H. Brady
|January 1975
|
|https://www.ams.org/journals/notices/197501/197501FullIssue.pdf<nowiki/>*
|}*A-25, PDF Page 109.

List of Busy Beaver Papers

2025-12-04T15:11:16Z

XnoobSpeakable: confirm date

{| class="wikitable"
|+
!Title
!Author
!Published
!DOI
!Download
|-
|On Non-Computable Functions
|T. Rado
|May 1962
|10.1002/j.1538-7305.1962.tb00480.x
|
|-
|On a simple source for non-computable functions
|T. Rado
|1963
|
|https://docs.bbchallenge.org/papers/Rado1963.pdf
|-
|A lower bound RADO's sigma function for binary turing machines
|Milton W. Green
|1964 November
11-13
|10.1109/SWCT.1964.3
|
|-
|Solutions of restricted cases of the halting problem applied to the determination of particular values of a non-computable function
|Allen H. Brady
|10 December 1964
|
|http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/zk51vk21c
|-
|The Conjectured Highest Scoring Machines for Rado's Σ(k) for the Value k = 4
|Allen H. Brady
|31 October 1966
|10.1109/PGEC.1966.264572
|
|-
|The solution to Rado's busy beaver game is now decided for k = 4. Preliminary report. (Abstract)
|Allen H. Brady
|January 1975
|
|https://www.ams.org/journals/notices/197501/197501FullIssue.pdf<nowiki/>*
|}*A-25, PDF Page 109.

List of Busy Beaver Papers

2025-12-02T16:46:51Z

XnoobSpeakable: new abstract

{| class="wikitable"
|+
!Title
!Author
!Published
!DOI
!Download
|-
|On Non-Computable Functions
|T. Rado
|May 1962
|10.1002/j.1538-7305.1962.tb00480.x
|
|-
|On a simple source for non-computable functions
|T. Rado
|1963
|
|https://docs.bbchallenge.org/papers/Rado1963.pdf
|-
|A lower bound RADO's sigma function for binary turing machines
|Milton W. Green
|1964*
|10.1109/SWCT.1964.3
|
|-
|Solutions of restricted cases of the halting problem applied to the determination of particular values of a non-computable function
|Allen H. Brady
|10 December 1964
|
|http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/zk51vk21c
|-
|The Conjectured Highest Scoring Machines for Rado's Σ(k) for the Value k = 4
|Allen H. Brady
|31 October 1966
|10.1109/PGEC.1966.264572
|
|-
|The solution to Rado's busy beaver game is now decided for k = 4. Preliminary report. (Abstract)
|Allen H. Brady
|January 1975
|
|https://www.ams.org/journals/notices/197501/197501FullIssue.pdf<nowiki/>**
|}
<nowiki>*</nowiki>(Possibly between November 11th and November 13th, could not locate source)

<nowiki>**</nowiki>A-25, PDF Page 109.

List of Busy Beaver Papers

2025-12-02T16:14:47Z

XnoobSpeakable: paper by Green

{| class="wikitable"
|+
!Title
!Author
!Published
!DOI
!Download
|-
|On Non-Computable Functions
|T. Rado
|May 1962
|10.1002/j.1538-7305.1962.tb00480.x
|
|-
|On a simple source for non-computable functions
|T. Rado
|1963
|
|https://docs.bbchallenge.org/papers/Rado1963.pdf
|-
|A lower bound RADO's sigma function for binary turing machines
|Milton W. Green
|1964*
|10.1109/SWCT.1964.3
|
|-
|Solutions of restricted cases of the halting problem applied to the determination of particular values of a non-computable function
|Allen H. Brady
|10 December 1964
|
|http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/zk51vk21c
|-
|The Conjectured Highest Scoring Machines for Rado's Σ(k) for the Value k = 4
|Allen H. Brady
|31 October 1966
|10.1109/PGEC.1966.264572
|
|}
<nowiki>*</nowiki>(Possibly between November 11th and November 13th, could not locate source)

List of Busy Beaver Papers

2025-12-02T16:02:22Z

XnoobSpeakable: add paper

List of Busy Beaver Papers

2025-12-02T15:51:25Z

XnoobSpeakable: Rado paper

{| class="wikitable"
|+
!Title
!Author
!Published
!DOI
!Download
|-
|On Non-Computable Functions
|T. Rado
|May 1962
|10.1002/j.1538-7305.1962.tb00480.x
|
|-
|Solutions of restricted cases of the halting problem applied to the determination of particular values of a non-computable function
|Allen H. Brady
|10 December 1964
|
|http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/zk51vk21c
|-
|The Conjectured Highest Scoring Machines for Rado's Σ(k) for the Value k = 4
|Allen H. Brady
|31 October 1966
|10.1109/PGEC.1966.264572
|
|}

List of Busy Beaver Papers

2025-12-02T15:47:03Z

XnoobSpeakable: Added paper

{| class="wikitable"
|+
!Title
!Author
!Published
!DOI
!Download
|-
|Solutions of restricted cases of the halting problem applied to the determination of particular values of a non-computable function
|Allen H. Brady
|10 December 1964
|
|http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/zk51vk21c
|-
|The Conjectured Highest Scoring Machines for Rado's Σ(k) for the Value k = 4
|Allen H. Brady
|31 October 1966
|10.1109/PGEC.1966.264572
|
|-
|
|
|
|
|
|}

List of Busy Beaver Papers

2025-12-02T15:44:31Z

XnoobSpeakable: Starting this page, will attempt to add as many papers as I can find

{| class="wikitable"
|+
!Title
!Author
!Published
!DOI
|-
|The Conjectured Highest Scoring Machines for Rado's Σ(k) for the Value k = 4
|Allen H. Brady
|31 October 1966
|10.1109/PGEC.1966.264572
|-
|
|
|
|
|-
|
|
|
|
|}

User:XnoobSpeakable/Holdouts-temp

2025-11-15T11:20:27Z

XnoobSpeakable: Don't use this for now

UNTIL I UPDATE THIS PLEASE USE THE CHART HERE: [[User:RobinCodes/Work on BB Domains]] MADE BY ROBINCODES.

ONCE I UPDATE THIS, I WILL REVERT THIS EDIT WITH WHICH I HAVE BLANKED THE TABLE

User:XnoobSpeakable/Holdouts-temp

2025-11-02T20:41:41Z

XnoobSpeakable: outdated disclaimer

== Main tables: ==
Top table: compilation of finished work that is almost certainly correct. This table might miss out on more recent changes and small reduction, especially if unverified.

Bottom table: compilation of latest progress, even if from unfinished work. More representative of the current state of the various BB domains, however, more likely to include mistakes or unverified work.

Note that both tables are full of compromises, some of which are explained in the footnotes. Soon there will be more tables in the "Specialized Tables" section that should solve this problem.

'''If you must refer to a single table, you probably want to use the bottom table. The top table can be very outdated.'''

CURRENTLY BOTH ARE LIKELY OUTDATED, I WILL UPDATE NOVEMBER 3RD
{| class="wikitable"
|+Number of holdouts (latest exact counts)
!
!2-state
!3-state
!4-state
!5-state
!6-state
!7-state
|-
!2-symbol
|0<ref name=":2" />
|0<ref name=":2" />
|0<ref name=":2" />
|0<ref name=":2">https://arxiv.org/pdf/2509.12337</ref>
|1618*<ref name=":4" />
|20,405,295<ref name=":3">https://drive.google.com/drive/folders/1-_JHOR89vCIH9RzwDCcoX8JHIz2GwRn0?usp=drive_link</ref>
|-
!3-symbol
|0<ref name=":2" />
|6**<ref name=":5">[[BB(3,3)]]</ref>
|9,401,447<ref name=":6">[[BB(4,3)]]</ref>
|
|
|
|-
!4-symbol
|0<ref name=":2" />
|15,136,283<ref name=":3" />
|
|
|
|
|-
!5-symbol
|75<ref name=":0">https://discord.com/channels/960643023006490684/1259770421046411285/1411512242498961458</ref>
|
|
|
|
|
|-
!6-symbol
|870,085<ref name=":1">https://discord.com/channels/960643023006490684/1084047886494470185/1424584096818135072</ref>
|
|
|
|
|
|}
<nowiki>*</nowiki>This count is based on equivalence classes. For the top table, the amount of individual unsolved TMs in TNF is currently 3067. The holdouts for every other entry use the unsolved TNF TM count.
{| class="wikitable"
|+Number of holdouts (in-progress and approximate values)
!
!2-state
!3-state
!4-state
!5-state
!6-state
!7-state
|-
!2-symbol
|0<ref name=":2" />
|0<ref name=":2" />
|0<ref name=":2" />
|0<ref name=":2" />
|1615*'''◊''' / 3063*'''◊'''<ref name=":4">https://discord.com/channels/960643023006490684/1239205785913790465/1429892916763033601</ref><ref name=":8">https://discord.com/channels/960643023006490684/1421782442213376000/1431483206208852001</ref><ref name=":7">https://discord.com/channels/960643023006490684/1239205785913790465/1431299260099461140</ref>
|20,405,295<ref name=":3" />
|-
!3-symbol
|0<ref name=":2" />
|6**<ref name=":5" />
|9,401,447<ref name=":6" />
|
|
|
|-
!4-symbol
|0<ref name=":2" />
|15,136,283<ref name=":3" />
|
|
|
|
|-
!5-symbol
|75 / 64'''†'''<ref name=":0" /><ref>https://discord.com/channels/960643023006490684/1259770421046411285/1428501877947109437</ref>
|
|
|
|
|
|-
!6-symbol
|870,083'''††'''<ref name=":1" />
|
|
|
|
|
|}
'''Other technicalities:'''

<nowiki>**</nowiki>This addendum applies to both tables. For BB(3,3), the most commonly accepted value is 6 holdouts<ref>https://discord.com/channels/960643023006490684/1084047886494470185/1421447666889523260</ref>, however, there are other values that I want to highlight in the table below:
{| class="wikitable"
!BB(3,3) holdouts
!Unproven
!Proven
|-
!By TNF
|6<ref name=":5" />
|9<ref name=":5" />
|-
!By Equivalence Classes
|4<ref name=":5" />
|7<ref name=":5" />
|}
'''†'''Formal / Informal.

'''◊'''For BB(6), it is quite difficult to keep track of in-progress holdout changes, as they are usually posted sporadically or not posted at all. I cannot guarantee the accuracy of these values in the 2nd table. Also note that in table 1, the values are proven (formally verified), but in table 2, some fraction of the reduction in holdouts might be formally verified, while the rest won't be. BB(6) also has the same problem as BB(3,3), with multiple conflicting values, however, I could not find a consensus for the most commonly accepted one.
{| class="wikitable"
!BB(6) holdouts
!Unproven
!Proven
|-
!By TNF
|3063<ref name=":4" /><ref name=":8" /><ref name=":7" />
|3067<ref name=":4" />
|-
!By Equivalence Classes
|1615<ref name=":4" /><ref name=":8" /><ref name=":7" />
|1618<ref name=":4" />
|}
'''††'''The top two halters have not been solved by automated tools and so are not part of the 870,085 holdouts list, but they are indeed known to halt.<ref>[[BB(2,6)]]</ref>

(A great source for holdouts lists is [https://drive.google.com/drive/folders/1-_JHOR89vCIH9RzwDCcoX8JHIz2GwRn0?usp=drive_link tjligocki's Google Drive folder])
<references />

== Specialized tables: ==
Coming eventually

Talk:TMBR: October 2025

2025-10-28T19:35:49Z

XnoobSpeakable: Created page with "Holdouts table seems to have some columns mixed up, please double-check ~~~~"

Holdouts table seems to have some columns mixed up, please double-check [[User:XnoobSpeakable|XnoobSpeakable]] ([[User talk:XnoobSpeakable|talk]]) 19:35, 28 October 2025 (UTC)

BB(3,4)

2025-10-27T17:39:37Z

XnoobSpeakable: Collapsible phase 1 section

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

<div class="toccolours mw-collapsible mw-collapsed">'''Phase 1 Info'''<div class="mw-collapsible-content">
Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.
</div></div>

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stage 3 is a lr_enum_continue computation to 1 million steps. Lúkos did not contribute to computing stage 3, but rather created a Python script to compute it in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 100000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>
</div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

BB(3,4)

2025-10-27T17:37:46Z

XnoobSpeakable: /* Phase 2 */ Remove links on some usernames as they already exist in a section above

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
XnoobSpeakable and Lúkos are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stage 3 is a lr_enum_continue computation to 1 million steps. Lúkos did not contribute to computing stage 3, but rather created a Python script to compute it in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 100000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>
</div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

User:XnoobSpeakable/Xnoobs-testing-page

2025-10-27T17:33:59Z

XnoobSpeakable: blanked out page

BB(3,4)

2025-10-27T17:31:44Z

XnoobSpeakable: Update to version from https://wiki.bbchallenge.org/wiki/User:XnoobSpeakable/Xnoobs-testing-page

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
[[User:XnoobSpeakable|XnoobSpeakable]] and [[User:WarpedWartWars|Lúkos]] are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stage 3 is a lr_enum_continue computation to 1 million steps. Lúkos did not contribute to computing stage 3, but rather created a Python script to compute it in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 100000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>
</div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]

User:XnoobSpeakable/Xnoobs-testing-page

2025-10-27T17:30:41Z

XnoobSpeakable: /* Top Halters */ credited 10^^2048 tm

BB(3,4) test:

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
[[User:XnoobSpeakable|XnoobSpeakable]] and [[User:WarpedWartWars|Lúkos]] are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stage 3 is a lr_enum_continue computation to 1 million steps. Lúkos did not contribute to computing stage 3, but rather created a Python script to compute it in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 100000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>
</div></div>

User:XnoobSpeakable/Holdouts-temp

2025-10-27T17:29:32Z

XnoobSpeakable: BB6

== Main tables: ==
Top table: compilation of finished work that is almost certainly correct. This table might miss out on more recent changes and small reduction, especially if unverified.

Bottom table: compilation of latest progress, even if from unfinished work. More representative of the current state of the various BB domains, however, more likely to include mistakes or unverified work.

Note that both tables are full of compromises, some of which are explained in the footnotes. Soon there will be more tables in the "Specialized Tables" section that should solve this problem.

'''If you must refer to a single table, you probably want to use the bottom table. The top table can be very outdated.'''
{| class="wikitable"
|+Number of holdouts (latest exact counts)
!
!2-state
!3-state
!4-state
!5-state
!6-state
!7-state
|-
!2-symbol
|0<ref name=":2" />
|0<ref name=":2" />
|0<ref name=":2" />
|0<ref name=":2">https://arxiv.org/pdf/2509.12337</ref>
|1618*<ref name=":4" />
|20,405,295<ref name=":3">https://drive.google.com/drive/folders/1-_JHOR89vCIH9RzwDCcoX8JHIz2GwRn0?usp=drive_link</ref>
|-
!3-symbol
|0<ref name=":2" />
|6**<ref name=":5">[[BB(3,3)]]</ref>
|9,401,447<ref name=":6">[[BB(4,3)]]</ref>
|
|
|
|-
!4-symbol
|0<ref name=":2" />
|15,136,283<ref name=":3" />
|
|
|
|
|-
!5-symbol
|75<ref name=":0">https://discord.com/channels/960643023006490684/1259770421046411285/1411512242498961458</ref>
|
|
|
|
|
|-
!6-symbol
|870,085<ref name=":1">https://discord.com/channels/960643023006490684/1084047886494470185/1424584096818135072</ref>
|
|
|
|
|
|}
<nowiki>*</nowiki>This count is based on equivalence classes. For the top table, the amount of individual unsolved TMs in TNF is currently 3067. The holdouts for every other entry use the unsolved TNF TM count.
{| class="wikitable"
|+Number of holdouts (in-progress and approximate values)
!
!2-state
!3-state
!4-state
!5-state
!6-state
!7-state
|-
!2-symbol
|0<ref name=":2" />
|0<ref name=":2" />
|0<ref name=":2" />
|0<ref name=":2" />
|1615*'''◊''' / 3063*'''◊'''<ref name=":4">https://discord.com/channels/960643023006490684/1239205785913790465/1429892916763033601</ref><ref name=":8">https://discord.com/channels/960643023006490684/1421782442213376000/1431483206208852001</ref><ref name=":7">https://discord.com/channels/960643023006490684/1239205785913790465/1431299260099461140</ref>
|20,405,295<ref name=":3" />
|-
!3-symbol
|0<ref name=":2" />
|6**<ref name=":5" />
|9,401,447<ref name=":6" />
|
|
|
|-
!4-symbol
|0<ref name=":2" />
|15,136,283<ref name=":3" />
|
|
|
|
|-
!5-symbol
|75 / 64'''†'''<ref name=":0" /><ref>https://discord.com/channels/960643023006490684/1259770421046411285/1428501877947109437</ref>
|
|
|
|
|
|-
!6-symbol
|870,083'''††'''<ref name=":1" />
|
|
|
|
|
|}
'''Other technicalities:'''

<nowiki>**</nowiki>This addendum applies to both tables. For BB(3,3), the most commonly accepted value is 6 holdouts<ref>https://discord.com/channels/960643023006490684/1084047886494470185/1421447666889523260</ref>, however, there are other values that I want to highlight in the table below:
{| class="wikitable"
!BB(3,3) holdouts
!Unproven
!Proven
|-
!By TNF
|6<ref name=":5" />
|9<ref name=":5" />
|-
!By Equivalence Classes
|4<ref name=":5" />
|7<ref name=":5" />
|}
'''†'''Formal / Informal.

'''◊'''For BB(6), it is quite difficult to keep track of in-progress holdout changes, as they are usually posted sporadically or not posted at all. I cannot guarantee the accuracy of these values in the 2nd table. Also note that in table 1, the values are proven (formally verified), but in table 2, some fraction of the reduction in holdouts might be formally verified, while the rest won't be. BB(6) also has the same problem as BB(3,3), with multiple conflicting values, however, I could not find a consensus for the most commonly accepted one.
{| class="wikitable"
!BB(6) holdouts
!Unproven
!Proven
|-
!By TNF
|3063<ref name=":4" /><ref name=":8" /><ref name=":7" />
|3067<ref name=":4" />
|-
!By Equivalence Classes
|1615<ref name=":4" /><ref name=":8" /><ref name=":7" />
|1618<ref name=":4" />
|}
'''††'''The top two halters have not been solved by automated tools and so are not part of the 870,085 holdouts list, but they are indeed known to halt.<ref>[[BB(2,6)]]</ref>

(A great source for holdouts lists is [https://drive.google.com/drive/folders/1-_JHOR89vCIH9RzwDCcoX8JHIz2GwRn0?usp=drive_link tjligocki's Google Drive folder])
<references />

== Specialized tables: ==
Coming eventually

User:XnoobSpeakable/Xnoobs-testing-page

2025-10-27T17:27:44Z

XnoobSpeakable: don't need categories on a testing page

BB(3,4) test:

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|???
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
[[User:XnoobSpeakable|XnoobSpeakable]] and [[User:WarpedWartWars|Lúkos]] are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stage 3 is a lr_enum_continue computation to 1 million steps. Lúkos did not contribute to computing stage 3, but rather created a Python script to compute it in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 100000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>
</div></div>

User:XnoobSpeakable/Xnoobs-testing-page

2025-10-27T17:25:14Z

XnoobSpeakable: stuff

BB(3,4) test:

The Busy Beaver problem for 3 states and 4 symbols is unsolved, with the existence of [[Cryptids]] in the domain being given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current BB(3,4) [[Champions#3-Symbol TMs|champion]] is {{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}. It runs for <math>2 \uparrow^{15} 5</math> steps before halting. It was discovered by Pavel Kropitz in 2024 and was analysed by Shawn Ligocki in the same year.

== Top Halters ==
The top 20 known longest running halting BB(3,4) TMs are:
{| class="wikitable"
|+
!Standard format
!(approximate) runtime
!Discoverer
|-
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|<math>2 \uparrow^{15} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB1RZ1LA2RB_1RC3RC1LA2LB_2LB2RC1LC3RB|halt}}
|<math>2 \uparrow^{12} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_3LA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 5</math>
|Pavel Kropitz
|-
|{{TM|1RB3RB1LC2LA_2LA2RB1LB3RA_1RA1RZ1LC2RA}}
|<math>2 \uparrow^{6} 4</math>
|Pavel Kropitz
|-
|{{TM|1RB0LB1RZ3LA_0LC3RB3RC1LB_2RB2LA3RA1LC|halt}}
|<math>10 \uparrow\uparrow {2\,048}</math>
|???
|-
|{{TM|1RB1RZ1LA2RB_2RC3RC3LB2RA_2LB3RB3LC1LA|halt}}
|<math>10 \uparrow\uparrow {189.05690}</math>
|[[User:XnoobSpeakable|XnoobSpeakable]]
|-
|{{TM|1RB3LA1RA2LB_2LC1RA2RC3RB_1RZ1LA2RA3RA|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LB2LA3LC_1LA2RB3RA1LB_1RZ1RB2LB3LB|halt}}
|<math>10 \uparrow\uparrow {188.16168}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA3LA3RB_2LC2RC1LB2RA_2RA2RB0LB1RZ|halt}}
|<math>10 \uparrow\uparrow {149.57147}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC2LC1LC_2LA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LB1RZ3LA_1LA3RC3LB1LC_2RA3RC0RA1LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LC1RC2RA_1LA3RA2RB1RZ_3LB2LC1RA0LB|halt}}
|<math>10 \uparrow\uparrow {130.20142}</math>
|[[User:WarpedWartWars|Lúkos]]
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ0LA|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB1RA1LB3RA_1RC3LB1LC1RC_2LA2RA1RZ1RB|halt}}
|<math>10 \uparrow\uparrow {96.06390}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA1LA0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB3LC0RA1RC_2LA1RZ3LA2RB_3LA0RA3LB0RA|halt}}
|<math>10 \uparrow\uparrow {95.24590}</math>
|XnoobSpeakable
|-
|{{TM|1RB2LA1RA1RC_1LA3LC3RB1RC_3LA1RZ3LB2RC|halt}}
|<math>10 \uparrow\uparrow {84.19957}</math>
|XnoobSpeakable
|-
|{{TM|1RB0LB1RA2LB_2RC3LB3RB2LA_2LC1RZ1LA2RB|halt}}
|<math>10 \uparrow\uparrow {76.17604}</math>
|XnoobSpeakable
|-
|{{TM|1RB1LA1RZ0LB_2LC2LB1RC1RB_3LA3LC0LC0RA|halt}}
|<math>10 \uparrow\uparrow {74.18390}</math>
|XnoobSpeakable
|-
|{{TM|1RB2RA1LA1LB_2RC3RB1RZ3LC_2LA1RC1RB0RA|halt}}
|<math>10 \uparrow\uparrow {69.55341}</math>
|Lúkos
|}

== Phase 1 ==
The initial phase of enumeration and reduction of [[holdouts]] took place in December 2024 and was done by Terry Ligocki using the Ligockis' C++ and Python codes. The initial enumerations generated 600,253,156,787 TMs of which 42,391,877,333 were holdout TMs. Also found were 202,014,400,019 halting TMs and 355,846,879,435 infinite TMs. The number of holdouts was reduced to 434,787,751 TMs (a 98.97% reduction).

Two C++ programs were run before the filters in the table.
<pre>
lr_enum 3 4 8 /dev/null /dev/null 3x4.unk.txt false
00 <= XX < 47: lr_enum_continue 3x4.in.XX 1000 /dev/null /dev/null 3x4.unk.txt.XX XX false
</pre>
Both do the initial enumeration and simple filtering. The "/dev/null" in both commands would be files where the halting and infinite TMs would be stored. The first command generates the TMs from a TNF tree for BB(3,4) of depth 8 and outputs the holdouts to 3x4.unk.txt. This file was then divided into 48 pieces, 3x4.in.XX, 0 <= XX < 47. The second commands (one for each XX) continues the enumeration by running each TM for 1,000 steps. It classifies each as halting, infinite, or unknown/holdout. Again, the halting and infinite TMs are "written" to /dev/null, i.e., they aren't saved. The holdouts are stored in 48 files: 3x4.unk.txt.XX.

For these runs the first command generated a total of 22,366,747 TMs: 932,198 halting, 235,446 infinite, and 21,199,103 holdouts. The second took the 22,366,747 holdout TMs and generated a total of 600,253,156,787 TMs: 202,014,400,019 halting, 355,846,879,435 infinite, and 42,391,877,333 holdouts. These holdouts were used as a starting point of the filters below.

The "Description" column in the table below contain the command run. Two options are not given, "--infile=..." and an "--outfile=...". These are necessary and specify where to read and write the results, respectively. Note: The work flow was to divide the input holdouts into 48 pieces, run the command on each piece simultaneously on one of 48 cores, and then combine the 48 results into a group of holdouts.

The details are given in this table:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Runtime (hours),
<math>*^3</math>= Decided,
<math>*^4</math>= Processed)

{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |<math>*^1</math>
!rowspan="2" |<math>*^2</math>
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Data
|-
!Input
!Output
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:left" |Terry Ligocki
|42,391,877,333
|32,247,381,725
|23.93%
|788.0
|3,576.08
|14,943.74
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="8" style="text-align:left" |[https://drive.google.com/drive/folders/1EsFw5DOjjZ6Xzjc8QgRa2YkInrsmFnLX?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|32,247,381,725
|12,789,441,316
|60.34%
|6,185.2
|873.85
|1,448.22
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,789,441,316
|4,332,283,583
|66.13%
|4,771.0
|492.39
|744.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,332,283,583
|2,796,143,404
|35.46%
|7,873.1
|54.20
|152.85
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,796,143,404
|1,398,734,288
|49.98%
|10,239.4
|37.91
|75.85
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --time=10 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,398,734,288
|764,851,053
|45.32%
|3,203.1
|54.97
|121.30
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.01 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|764,851,053
|581,654,405
|23.95%
|1,925.3
|26.43
|110.35
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=12 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|581,654,405
|434,787,751
|25.25%
|9,042.5
|4.51
|17.87
|style="text-align:left" |CPS_Filter.py --min-block-size=4 --max-block-size=6 --max-steps=10_000
|}

== Phase 2 ==
[[User:XnoobSpeakable|XnoobSpeakable]] and [[User:WarpedWartWars|Lúkos]] are working on applying mxdys' deciders/parameters to the remaining holdouts. The previous holdouts list by Terry Ligocki was split up into 8696 files containing 50,000 holdouts each* (*the last one actually has 37,751) and the deciders were applied to the files individually. These files can be called subtasks. Lúkos made a Python script to compute the subtasks in parallel, based off of XnoobSpeakable's earlier imperfect script.

Certain data such as TMs/sec/core is unavailable, because the amount of time the computation took was not kept track of.

Stage 3 is a lr_enum_continue computation to 1 million steps. Lúkos did not contribute to computing stage 3, but rather created a Python script to compute it in bulk, which XnoobSpeakable used.

For the "Contribution" column, the first number is the amount of subtasks solved by XnoobSpeakable, the 2nd is the amount solved by Lúkos. Note that the counts are unequal, because Lúkos has a slower CPU with a lower core count. According to XnoobSpeakable, the time contribution from both contributors is roughly equal. Lúkos also worked on the Python scripts used, while XnoobSpeakable worked on compiling holdouts lists and finding optimal deciders to apply.

[[User:Peacemaker II|Peacemaker II]] worked on verifying the validity of the results as well as providing solved TM counts per decider. Stages 1, 2, and 4 have been validated - no dropped TMs. XnoobSpeakable verified stage 6.

The details will be given in this table:

{| class="wikitable sortable" style="text-align: left"
! rowspan="2" |Done by
! colspan="2" |Holdout TMs
! rowspan="2" |% Reduced
! rowspan="2" |Description
! rowspan="2" |Subtasks
! rowspan="2" |Contribution
! rowspan="2" |Data
|-
!Input
!Output
|-
| style="text-align:left" |XnoobSpeakable, Lúkos
|434,787,751
|64,777,377
|85.1%
| style="text-align:left" |Phase 2 stage 1
|8696
|7696 / 1000
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|64,777,377
|37,016,957
|42.9%
|Phase 2 stage 2
|1296
|1000 / 296
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable
|37,016,957
|26,266,261
|29.0%
|Phase 2 stage 3
|741
|741 / 0
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|26,266,261
|22,396,711
|14.7%
|Phase 2 stage 4
|526
|485 / 41
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|22,396,711
|17,983,810
|19.7%
|Phase 2 stage 5
|448
|390 / 58
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|17,983,810
|15,564,491
|13.5%
|Phase 2 stage 6
|360
|300 / 60
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|-
|XnoobSpeakable, Lúkos
|15,564,491
|15,136,283
|2.75%
|Phase 2 stage 7
|312
|260 / 52
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i Google Drive]
|}

== Phase 2 Data ==
Here we will list the deciders applied during the various stages of Phase 2. Each decider within a stage was not applied in a specific order. Some stages have a number of TMs solved by every decider at the end of each row, provided by Peacemaker II.

<div class="toccolours mw-collapsible mw-collapsed">'''Details'''<div class="mw-collapsible-content">
Phase 2 stage 1:
<pre>
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 2 run 86569103
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 1000 NG_n 1 run 26093656
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 13972946
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 2 run 7190617
chr_LRUH 10 chr_H 6 MitM_CTL NG maxT 1000 NG_n 2 run 90302784
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 4 run 4342619
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 12 H 0 tH 1 n 2 run 11764327
chr_LRUH 2 chr_H 2 MitM_CTL NG maxT 1000 NG_n 1 run 55465842
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 2 n 1 run 17805678
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 2 H 0 tH 0 n 1 run 12623067
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 2240499
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 1 tH 1 n 2 run 10223131
chr_LRUH 6 chr_H 4 MitM_CTL NG maxT 10000 NG_n 1 run 2901053
chr_LRUH 22 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 28515052
</pre>
Phase 2 stage 2:
<pre>
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 4 n 8 run 1030303
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 2 n 2 run 1465523
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 5232902
chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run 1720994
MitM_CTL RWL_mod sim 1001 maxT 3000 H 8 mod 3 n 2 run 555883
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 6 run 290547
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 1 run 67506
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 1577979
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 1604533
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 6 run 10012948
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 0 tH 0 n 4 run 526822
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 1 n 1 run 34821
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 3 run 356375
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 20 run 1970422
MitM_CTL RWL_mod sim 1001 maxT 1000 H 6 mod 3 n 1 run 443339
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 1 n 2 run 518824
MitM_CTL RWL_mod sim 1001 maxT 10000 H 2 mod 2 n 1 run 61865
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 1 n 2 run 288834
</pre>
Phase 2 stage 3 (lr_enum_continue from [https://github.com/sligocki/busy-beaver busy-beaver] for 1 million steps):
<pre>
lr_enum_continue ./in.txt 100000 ./halt.txt ./inf.txt ./unknown.txt "" false
</pre>
Phase 2 stage 4:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 2 run 202520
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run 559013
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run 1584
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 10000 NG_n 1 run 148544
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run 812666
chr_asth 0 chr_LRUH 48 chr_H 48 MitM_CTL NG maxT 10000 NG_n 3 run 2043171
MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 2 n 1 run 102052
</pre>
Phase 2 stage 5:
<pre>
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 10 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 1 tH 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 6 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 5 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 1 tH 0 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 2 mod 3 n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 5 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 4 mod 4 n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 0 tH 1 n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 1 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 3 n 1 run
chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 30000 NG_n 3 run
chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 8 H 2 tH 1 n 2 run
chr_asth 0 chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 16 H 1 tH 0 n 6 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 16 H 0 tH 0 n 1 run
chr_LRUH 6 chr_H 2 MitM_CTL NG maxT 10000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 3 H 1 tH 0 n 2 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 3 n 1 run
chr_LRUH 3 chr_H 1 MitM_CTL NG maxT 100000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 6 H 1 tH 0 n 4 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 2 mod 2 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 4 H 2 tH 0 n 1 run
chr_LRUH 4 chr_H 0 MitM_CTL NG maxT 1000 NG_n 2 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 2 mod 1 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 3 mod 6 n 1 run
chr_asth 0 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run
chr_asth 0 chr_LRUH 60 chr_H 60 MitM_CTL NG maxT 30000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 1 run
chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 4 H 1 tH 1 n 2 run
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run
chr_asth 0 chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 3000 NG_n 2 run
</pre>
Phase 2 stage 6:

XnoobSpeakable ran Enumerate.py with a 0.15s/TM time limit, Lúkos ran it with a 0.75s/TM time limit.
<pre>
python "+str(pl.Path("../../Code/Enumerate.py"))+" --infile="+str(pl.Path("./in.txt"))+" --outfile="+str(pl.Path("./out.pb"))+" --max-loops=990_000 --tape-limit=9_900 --no-steps --time="+str(time)+" --recursive --exp-linear-rules --lin-steps=0 --no-ctl --save-freq=10_000
</pre>
Phase 2 stage 7:
<pre>
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 3 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 5 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 3 H 0 tH 0 n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_LRUH 2 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 4 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 16 H 0 tH 1 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 2 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 4 H 0 tH 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 16 H 0 tH 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 12 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 30000 H 1 mod 2 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 0 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 3 n 1 run
MitM_CTL RWL_mod sim 1001 maxT 3000 H 1 mod 1 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 2 H 0 tH 0 n 1 run
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 0 n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 3000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 1000 NG_n 1 run
chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 1 run
MitM_CTL RWL_mod sim 1001 maxT 10000 H 1 mod 1 n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 1 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 100000 NG_n 2 run
chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 1 run
</pre>
</div></div>
[[Category:BB Domains]][[Category:BB(3,4)]]