BusyBeaverWiki - User contributions [en]

BB(4,3)

2025-10-17T00:48:37Z

Konkhra: not 392 infinite TMs, but 392B infinite TMs

The Busy Beaver problem for 4 states and 3 symbols is unsolved. The existence of [[Cryptids]] in the domain is given by the discovery of [[Bigfoot]] in [[BB(3,3)]]. The current [[Champions#3-Symbol TMs|champion]] appears to be {{TM|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD|halt}} which was discovered by Pavel Kropitz in May 2024 and analyzed by Racheline in Feb 2025, demonstrating the lower bounds:

<math display="block">S(4,3) > \Sigma(4,3) > 2 \uparrow\uparrow\uparrow 2^{2^{32}}</math>

The exact status of championship currently remains unclear because of this list of "Potential Champions" below which has not yet been fully investigated.

== Top Halters ==
{{Incomplete List}}
The longest running halting BB(4,3) TMs are split amongst two classes: the pentational TMs found by Pavel Kropitz outlined in the Potential Champions section, and the tetrational TMs found by comprehensive holdout filtering by Andrew Ducharme. The scores are given using [[wikipedia:Knuth's_up-arrow_notation|Knuth's up-arrow notation]] with an extension to decimal tetration<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/06/25/ext-up-notation.html "Extending Up-arrow Notation"]</ref>. The current champion is:
{| class="wikitable"
!Standard format
!(approximate) runtime
|-
|{{TM|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD|halt}}
|<math>2 \uparrow\uparrow\uparrow 2^{2^{32}}</math>
|}
The longest running halters found by comprehensive search are:
{| class="wikitable"
|+
!Standard format
!Approximate sigma score
|-
|{{TM|1RB2LD2LA_1RC0RD2LA_1LA1RZ0LC_2RD2RC0LD|halt}}
|10 ↑↑ 53.22643
|-
|{{TM|1RB0LB1RD_2LC1RZ1LB_2LD0LC1RB_2RA2RD1LD|halt}}
|10 ↑↑ 42.44165
|-
|{{TM|1RB2RD1LA_2RC1RB1RA_1LC1RZ1LD_2RA2LD0LA|halt}}
|10 ↑↑ 33.62777
|-
|{{TM|1RB1LD2LA_1LC1RZ2RD_2LA2RA0LD_2RD0RB0LC|halt}}
|10 ↑↑ 33.20324
|-
|{{TM|1RB1RZ0RD_1LC0RC0LD_2LC2LA0RB_2RB1RD2RD|halt}}
|10 ↑↑ 33.16838
|-
|{{TM|1RB2LC1LB_2LA2RD0RC_2LB0LA1RB_1RZ2RB2LA|halt}}
|10 ↑↑ 32.00113
|-
|{{TM|1RB0RC2RA_1LC2RC0RC_2LC2LD0RB_1RA1RZ0RC|halt}}
|10 ↑↑ 27.14142
|-
|{{TM|1RB0LD0RA_1RC1RZ0RB_1LA1RD2RC_2LD2LB0RD|halt}}
|10 ↑↑ 21.74030
|-
|{{TM|1RB2RC1RD_2RC0RD1LD_1LA1RZ2RB_2LB2LD1RA|halt}}
|10 ↑↑ 21.41425
|-
|{{TM|1RB2LC2LA_1LC0RA1LC_1LA2RD1LB_1RZ2RC0RA|halt}}
|10 ↑↑ 20.07678
|}

== Potential Champions ==
In May 2024, Pavel Kropitz found 7 halting TMs that run for a large number of steps, but have not been analyzed in detail:

https://discord.com/channels/960643023006490684/1026577255754903572/1243253180297646120

'''Current champion and equivalent TMs:'''

* The current champion {{TM|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD|halt}}: 1 2^((80*2^((<(8*2^((8*2^(29) - 2)) - 5); (<(80*2^((b - 10)/5) - 17)/9; (40*2^((8*2^((a - 11)/5) - 2)) - 4); (40*2^(2) - 4)> + 4); (<(80*2^((<(80*2^((8*2^((8*2^(29) - 2)) - 3)) - 13)/9; (40*2^((8*2^((a - 11)/5) - 2)) - 4); (40*2^(2) - 4)> - 6)/5) - 17)/9; (40*2^((8*2^((a - 11)/5) - 2)) - 4); (40*2^(2) - 4)> + 4)> - 10)/5) - 3)) 1 0 1 2 1^2 Z> 1 2^2 1
* {{TM|0RB1RZ1RC_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD|halt}}: 1 2^((80*2^((<(8*2^((8*2^(29) - 2)) - 5); (<(80*2^((b - 10)/5) - 17)/9; (40*2^((8*2^((a - 11)/5) - 2)) - 4); (40*2^(2) - 4)> + 4); (<(80*2^((<(80*2^((8*2^((8*2^(29) - 2)) - 3)) - 13)/9; (40*2^((8*2^((a - 11)/5) - 2)) - 4); (40*2^(2) - 4)> - 6)/5) - 17)/9; (40*2^((8*2^((a - 11)/5) - 2)) - 4); (40*2^(2) - 4)> + 4)> - 10)/5) - 3)) 1 0 1 2 1^2 Z> 1 2^2 1
* {{TM|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ0RA|halt}}: 1 2^((80*2^((<(8*2^((8*2^(29) - 2)) - 5); (<(80*2^((b - 10)/5) - 17)/9; (40*2^((8*2^((a - 11)/5) - 2)) - 4); (40*2^(2) - 4)> + 4); (<(80*2^((<(80*2^((8*2^((8*2^(29) - 2)) - 3)) - 13)/9; (40*2^((8*2^((a - 11)/5) - 2)) - 4); (40*2^(2) - 4)> - 6)/5) - 17)/9; (40*2^((8*2^((a - 11)/5) - 2)) - 4); (40*2^(2) - 4)> + 4)> - 10)/5) - 3)) 1 0 1 2 1^2 Z> 1 2^2 1
* {{TM|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ1RB|halt}}: 1 2^((80*2^((<(8*2^((8*2^(29) - 2)) - 5); (<(80*2^((b - 10)/5) - 17)/9; (40*2^((8*2^((a - 11)/5) - 2)) - 4); (40*2^(2) - 4)> + 4); (<(80*2^((<(80*2^((8*2^((8*2^(29) - 2)) - 3)) - 13)/9; (40*2^((8*2^((a - 11)/5) - 2)) - 4); (40*2^(2) - 4)> - 6)/5) - 17)/9; (40*2^((8*2^((a - 11)/5) - 2)) - 4); (40*2^(2) - 4)> + 4)> - 10)/5) - 3)) 1 0 1 2 1^2 Z> 1 2^2 1

'''Others:'''
* {{TM|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_2RB2RA2RD|halt}}: 1 Z> 1^((8*<7; (6*2^((4b + 14)) - 4); (6*2^((48*2^(21) - 2)) - 4)> + 33)) 2
* {{TM|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD|halt}}: 1 Z> 1^((2*<(<(<(16*2^(92) - 3); (24*2^((24*2^(<(b + 10); (24*2^(b) - 4); 2>) - 3)) - 11); (24*2^((24*2^(<(24*2^((24*2^(<(24*2^((24*2^(92) - 3)) - 2); (24*2^(b) - 4); 92>) - 3)) - 1); (24*2^(b) - 4); 2>) - 3)) - 11)> + 8)/3; (24*2^((24*2^(<(b + 10); (24*2^(b) - 4); 2>) - 3)) - 11); (24*2^((24*2^(<1; (24*2^(b) - 4); 2>) - 3)) - 11)> + 5)/3; (24*2^((24*2^(<(b + 10); (24*2^(b) - 4); 2>) - 3)) - 11); (24*2^((24*2^(<1; (24*2^(b) - 4); 2>) - 3)) - 11)> + 19))
* {{TM|1RB2LB0LB_2LC2LA0LA_2RD1LC1RZ_1RA2LD1RD|halt}}: 1 Z> 1^(162*3^((3*<(243*3^(6) - 5)/2; (<(54*3^((3b + 11)/2) - 2); (54*3^((3b + 14)/2) - 6); (54*3^(7) - 6)> + 1); (<(54*3^((3*<(54*3^(7) - 3); (54*3^((3b + 14)/2) - 6); (54*3^((81*3^(7) - 2)) - 6)> + 14)/2) - 2); (54*3^((3b + 14)/2) - 6); (54*3^(7) - 6)> + 1)> + 11)/2)) 2

== 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 ~633B(illion) TMs of which ~34.4B TMs were holdouts. Also found were ~206B halting TMs and ~392B infinite TMs. The number of holdouts were reduced to ~461M TMs (a 98.66% reduction).

Two C++ programs were run before the filters in the table.
<pre>
lr_enum 4 3 8 /dev/null /dev/null 4x3.unk.txt false
00 <= XX < 47: lr_enum_continue 4x3.in.XX 1000 /dev/null /dev/null 4x3.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(4,3) of depth 8 and outputs the holdouts to 4x3.unk.txt. This file was then divided into 48 pieces, 4x3.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: 4x3.unk.txt.XX.

For these runs the first command generated a total of ~45M TMs: ~1.86M halting, ~774K infinite, and ~42.0M holdouts. The second took the ~42.0M holdout TMs and generated a total of ~633B TMs: ~206B halting, ~392B infinite, and ~34.4B 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
|34,413,860,527
|30,874,934,791
|10.28%
|646.6
|1,520.36
|14,784.57
|style="text-align:left" |Reverse_Engineer_Filter.py
|rowspan="10" style="text-align:left" |[https://drive.google.com/drive/folders/1KMOVgngtUVMEA7EjxtNcsgksQ5Y4tby9?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|30,874,934,791
|12,942,386,396
|58.08%
|4,134.8
|1,204.72
|2,074.19
|style="text-align:left" |CPS_Filter.py --block-size=1
|-
|style="text-align:left" |Terry Ligocki
|12,942,386,396
|4,534,322,415
|64.97%
|3,361.1
|694.88
|1,069.62
|style="text-align:left" |CPS_Filter.py --block-size=2
|-
|style="text-align:left" |Terry Ligocki
|4,534,322,415
|2,959,598,830
|34.73%
|3,318.1
|131.83
|379.59
|style="text-align:left" |CPS_Filter.py --block-size=3
|-
|style="text-align:left" |Terry Ligocki
|2,959,598,830
|1,651,940,618
|44.18%
|2,700.6
|134.50
|304.42
|style="text-align:left" |Enumerate.py --max-loops=1_000 --block-size=2 --no-steps --time=0.002 --lin-steps=0 --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|1,651,940,618
|854,984,279
|48.24%
|2,276.3
|97.25
|201.59
|style="text-align:left" |Enumerate.py --max-loops=10_000 --block-size=12 --no-steps --time=0.005 --lin-steps=0 --no-ctl --no-reverse-engineer --save-freq=10_000
|-
|style="text-align:left" |Terry Ligocki
|854,984,279
|683,163,325
|20.10%
|430.1
|110.96
|552.15
|style="text-align:left" |CPS_Filter.py --block-size=4 --max-steps=1_000
|-
|style="text-align:left" |Terry Ligocki
|683,163,325
|460,916,384
|32.53%
|5,507.9
|11.21
|34.45
|style="text-align:left" |CPS_Filter.py --min-block-size=1 --max-block-size=6 --max-steps=10_000
|-
|style="text-align:center" |'''Cumulative'''
|'''632,656,365,801'''
|'''460,916,384'''
|'''98.66%'''
| ---
| ---
| ---
|style="text-align:left" | ---
|}

== Phase 2 ==

When Phase 1 was completed, a set of deciders/parameters were run to reduce the number of holdout TMs. The details are given in the various Stages below.

=== Stage 1 ===

Starting from the results of Phase 1, Terry Ligocki ran @mxdys' C++ code, "main.exe", using a variety of its deciders with various parameters. A total of 33 variations were run. The holdouts were reduced from ~461B TMs to ~33.9M TMs (a 92.7% reduction). The details are given in the table below, including links to the Google Drive with the holdouts. Entries with multiple lines represent runs where all the commands in the "Description" were applied during one run.

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Compute Time (core-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
|460,916,384
|234,834,703
|49.05%
|96.7
|649.48
|1,324.10
|style="text-align:left" | chr_LRUH 4 chr_H 2 MitM_CTL NG maxT 1000 NG_n 2 run
|rowspan="20" style="text-align:left" |[https://drive.google.com/drive/folders/1tFtg1eFC-AdqCzh7XNmx5O2mTQwtaNbm?usp=drive_link Google Drive]
|-
|style="text-align:left" |Terry Ligocki
|234,834,703
|160,518,206
|31.65%
|70.9
|291.33
|920.57
|style="text-align:left" | chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 1000 NG_n 2 run
|-
|style="text-align:left" |Terry Ligocki
|160,518,206
|132,296,033
|17.58%
|41.5
|188.86
|1,074.17
|style="text-align:left" | MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 6 n 1 run
|-
|style="text-align:left" |Terry Ligocki
|132,296,033
|113,193,595
|14.44%
|54.9
|96.57
|668.77
|style="text-align:left" | MitM_CTL RWL_mod sim 1001 maxT 1000 H 4 mod 1 n 6 run
|-
|style="text-align:left" |Terry Ligocki
|113,193,595
|85,920,795
|24.09%
|106.8
|70.96
|294.52
|style="text-align:left" | chr_LRUH 16 chr_H 12 MitM_CTL NG maxT 3000 NG_n 2 run
|-
|style="text-align:left" |Terry Ligocki
|85,920,795
|78,674,774
|8.43%
|28.9
|69.62
|825.51
|style="text-align:left" | MitM_CTL RWL_mod sim 1001 maxT 1000 H 8 mod 2 n 2 run
|-
|style="text-align:left" |Terry Ligocki
|78,674,774
|73,228,547
|6.92%
|68.7
|22.02
|318.04
|style="text-align:left" | MitM_CTL CPS_LRU sim 1001 maxT 3000 LRUH 8 H 1 tH 1 n 4 run
|-
|style="text-align:left" |Terry Ligocki
|73,228,547
|67,014,897
|8.49%
|23.2
|74.50
|878.02
|style="text-align:left" | chr_LRUH 4 chr_H 4 MitM_CTL NG maxT 30000 NG_n 1 run
|-
|style="text-align:left" |Terry Ligocki
|67,014,897
|57,625,231
|14.01%
|75.6
|34.49
|246.13
|style="text-align:left" | MitM_CTL RWL_mod sim 1001 maxT 3000 H 4 mod 2 n 6 run
|-
|style="text-align:left" |Terry Ligocki
|57,625,231
|48,070,606
|16.58%
|645.4
|4.11
|24.80
|style="text-align:left" | chr_LRUH 18 chr_H 12 MitM_CTL NG maxT 30000 NG_n 10 run
|-
|style="text-align:left" |Terry Ligocki
|48,070,606
|44,254,286
|7.94%
|166.3
|6.38
|80.31
|style="text-align:left" | MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 6 H 1 tH 1 n 12 run
|-
|style="text-align:left" |Terry Ligocki
|44,254,286
|40,836,159
|7.72%
|188.3
|5.04
|65.29
|style="text-align:left" | MitM_CTL RWL_mod sim 1001 maxT 100000 H 3 mod 1 n 2 run
|-
|style="text-align:left" |Terry Ligocki
|40,836,159
|37,460,692
|8.27%
|192.3
|4.88
|58.99
|style="text-align:left" |
chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 
MitM_CTL RWL_mod sim 1001 maxT 100000 H 2 mod 2 n 1 run 
MitM_CTL CPS_LRU sim 1001 maxT 1000 LRUH 6 H 0 tH 1 n 2 run 
MitM_CTL RWL_mod sim 1001 maxT 3000 H 6 mod 3 n 2 run 
chr_LRUH 6 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 
chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 10000 NG_n 2 run 
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 3000 NG_n 2 run 
MitM_CTL RWL_mod sim 1001 maxT 1000 H 3 mod 3 n 1 run 
MitM_CTL RWL_mod sim 1001 maxT 1000 H 8 mod 2 n 1 run 
MitM_CTL RWL_mod sim 1001 maxT 100000 H 3 mod 2 n 1 run 
|-
|style="text-align:left" |Terry Ligocki
|37,460,692
|36,167,570
|3.45%
|237.7
|1.51
|43.77
|style="text-align:left" |
MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 3 H 0 tH 1 n 2 run 
chr_LRUH 12 chr_H 12 MitM_CTL NG maxT 10000 NG_n 2 run 
chr_LRUH 14 chr_H 12 MitM_CTL NG maxT 10000 NG_n 4 run 
chr_LRUH 6 chr_H 6 MitM_CTL NG maxT 30000 NG_n 2 run 
chr_LRUH 10 chr_H 8 MitM_CTL NG maxT 10000 NG_n 4 run 
MitM_CTL RWL_mod sim 1001 maxT 3000 H 6 mod 2 n 2 run 
|-
|style="text-align:left" |Terry Ligocki
|36,167,570
|34,642,544
|4.22%
|467.2
|0.91
|21.50
|style="text-align:left" | MitM_CTL RWL_mod sim 1001 maxT 30000 H 3 mod 2 n 24 run
|-
|style="text-align:left" |Terry Ligocki
|34,642,544
|34,339,943
|0.87%
|383.1
|0.22
|25.12
|style="text-align:left" | MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 8 H 1 tH 0 n 24 run
|-
|style="text-align:left" |Terry Ligocki
|34,339,943
|33,860,069
|1.40%
|666.5
|0.20
|14.31
|style="text-align:left" | MitM_CTL CPS_LRU sim 1001 maxT 100000 LRUH 12 H 2 tH 2 n 8 run
|-
|style="text-align:center" |'''Cumulative'''
|'''460,916,384'''
|'''33,860,069'''
|'''92.70%'''
| ---
| ---
| ---
|style="text-align:left" | ---
|}

=== Stage 2 ===

Starting from the results of Phase 2 Stage, Terry Ligocki ran a variety of enumeration and decider codes. Some of these runs generated new TMs due to the BB(4,3) TNF tree not being fully generated at this time. These reduced the number of holdouts from ~33.9M TMs to ~12.0M TMs (a 64.6% reduction). The details are given in the table below, including links to the Google Drive with the holdouts, halting, and infinite TMs:

(done to reduce column size:
<math>*^1</math>= % Reduced,
<math>*^2</math>= Compute Time (core-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
|33,860,069
|21,065,769
|37.79%
|93.0
|38.20
|101.11
|style="text-align:left" |lr_enum_continue 4x3.in.txt 1000000 4x3.halt.txt 4x3.inf.txt 4x3.holdouts.txt 00 false
|rowspan="20" style="text-align:left" |
|-
|style="text-align:left" |Terry Ligocki
|21,065,769
|18,949,009
|10.05%
|5,566.1
|0.11
|1.05
|style="text-align:left" |Enumerate.py max-loops 100_000 block-size 2 --tape-limit 1_000 --no-steps --time 1.0 --recursive --exp-linear-rules --lin-steps 0 --no-ctl --no-reverse-engineer --infile 4x3.in.txt --outfile 4x3.out.pb
|-
|style="text-align:left" |Terry Ligocki
|18,949,009
|18,138,027
|4,28%
|0.4
|511.59
|11953.46
|style="text-align:left" |Reverse_Engineer_Filter.py --infile 4x3.in.txt --outfile 4x3.out.pb
|-
|style="text-align:left" |Terry Ligocki
|18,138,027
|11,985,999
|33.92%
|3.0
|571.85
|1685.99
|style="text-align:left" |chr_asth 0 chr_LRUH 1 chr_H 1 MitM_CTL NG maxT 100000 NG_n 3 run
|-
|style="text-align:center" |'''Cumulative'''
|'''33,860,069'''
|'''11,985,999'''
|'''64.60%'''
| ---
| ---
| ---
|style="text-align:left" | ---
|}

==References==

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

User talk:Hipparcos/Status by BB domain

2025-07-15T03:22:37Z

Konkhra:

Thank you! Status by BB domain - This is really useful and educational.--[[User:Konkhra|Konkhra]] ([[User talk:Konkhra|talk]]) 03:18, 15 July 2025 (UTC)

User talk:Hipparcos/Status by BB domain

2025-07-15T03:18:37Z

Konkhra: Created page with "Thank you! This is really useful and educational.--~~~~"

Thank you! This is really useful and educational.--[[User:Konkhra|Konkhra]] ([[User talk:Konkhra|talk]]) 03:18, 15 July 2025 (UTC)

BB(7)

2025-06-03T08:35:12Z

Konkhra: Why P. Michel????

The 7-state, 2-symbol Busy Beaver problem '''BB(7)''' is a mostly unexplored domain with only preliminary information.

The current BB(7) champion is {{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}} discovered by Pavel Kropitz in 2025 proving the lower bound:<math display="block">S(7) > \Sigma(7) > 2 \uparrow^{11} 2 \uparrow^{11} 3</math>

== History ==
Before 2025, the only known BB(7) champions were produced by hand, not by search. Example, Milton Green designed a machine in 1964 that had [[sigma score]] 22,961 and Wythagoras modified a BB(6) champion in 2014 to produce a machine that had sigma score <math>> 10 \uparrow\uparrow 5</math>.

In May 2025, mxdys shared [https://github.com/ccz181078/TM C++ code] that breaks up the BB(7) enumeration into 1 million subtasks which each run for about 2 minutes and leave ~100 holdouts each. Various folks on Discord have been investigating different sections of this domain to search for champions.

== Top Halters ==
Based on limited search through a subset of the 1 million subtasks from mxdys's code, the top 20 scoring known machines are:
{| class="wikitable"
!TM
!Approximate sigma score
!Discoverer
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|Pavel Kropitz
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286.17
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
|10 ↑↑ 246.32
|@Iijil
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LG_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RG0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ0RE}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LF0RF_0RA1RE_1RZ0RA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LD0RF_0RA1RE_1RZ0RA}}
|10 ↑↑ 188.28
|@XnoobSpeakable, @Peacemaker II
|-
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|10 ↑↑ 133
|@poppuncher
|-
|{{TM|1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF}}
|10 ↑↑ 129.24
|@Iijil
|-
|{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}}
|10 ↑↑ 116.97
|Terry Ligocki
|-
|{{TM|1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG}}
|10 ↑↑ 116.05
|
|-
|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ}}
|10 ↑↑ 115.52
|@prurq
|-
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|Shawn Ligocki
|-
|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 113.37
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|Andrew Ducharme
|-
|{{TM|1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ}}
|10 ↑↑ 93.78
|Terry Ligocki
|}
The top 20 known halters with unique scores are:
{| class="wikitable"
!TM
!Approximate sigma score
!Discoverer
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|Pavel Kropitz
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286.17
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
|10 ↑↑ 246.32
|@Iijil
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|10 ↑↑ 133
|@poppuncher
|-
|{{TM|1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF}}
|10 ↑↑ 129.24
|@Iijil
|-
|{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}}
|10 ↑↑ 116.97
|Terry Ligocki
|-
|{{TM|1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG}}
|10 ↑↑ 116.05
|
|-
|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ}}
|10 ↑↑ 115.52
|@prurq
|-
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|Shawn Ligocki
|-
|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 113.37
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|Andrew Ducharme
|-
|{{TM|1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ}}
|10 ↑↑ 93.78
|Terry Ligocki
|-
|{{TM|1RB1LB_1LC1RE_1RD1RC_0RE0RD_1LF0RB_1LF1LG_1RZ0LA}}
|10 ↑↑ 86.40
|Terry Ligocki
|-
|{{TM|1RB1LC_1RC0LG_1RD0RG_0LE0RA_1LC0LF_0LD1LF_1RZ1RA}}
|10 ↑↑ 82.44
|Terry Ligocki
|-
|{{TM|1RB1LC_1RC0RC_1RD1LA_0RE1RF_1LC0LG_1LA1LE_1RZ1LF}}
|10 ↑↑ 76.36
|Andrew Ducharme
|-
|{{TM|1RB0LD_1RC0RF_0RD1RA_1LE0RB_0LA0LB_1RA1RG_0RA1RZ}}
|10 ↑↑ 64.03
|Terry Ligocki
|-
|{{TM|1RB1RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_1RG1RZ_0LG0LE}}
|10 ↑↑ 63.56
|Terry Ligocki
|-
|{{TM|1RB0LD_1RC0RF_0RD1RA_1LE0RB_0LA0LB_1RA1RG_1LE1RZ}}
|10 ↑↑ 61.02
|Terry Ligocki
|}

== Current Progress ==
This is a summary of the 1 million subtasks from mxdys's code that have been processed, including further processing by Shawn Ligocki's linear rule code ("TBD" = "To Be Determined", "TBE" = "To Be Entered"):
{| class="wikitable defaultleft"
!rowspan="2"|Task range
!rowspan="2"|Done by
!colspan="2"|Completed
!rowspan="2"|# holdouts
!rowspan="2"|Maximum Score TM
!rowspan="2"|~Sigma
!rowspan="2"|Source
|-
!enumeration
!linear rule
|-
|00xxxx
|@Iijil
|Yes
|Yes
|728,495
|{{TM|1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC}}
|10 ↑↑ 46
| rowspan="10" |[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD Google Drive folder]
|-
|01xxxx
|@Iijil
|Yes
|Yes
|1,056,253
|TBD
|TBD
|-
|02xxxx
|@Iijil
|Yes
|No
|963,486
|TBD
|TBD
|-
|03xxxx
|@Iijil
|Yes
|No
|1,052,504
|TBD
|TBD
|-
|04xxxx
|@Iijil
|Yes
|No
|955,711
|TBD
|TBD
|-
|05xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|06xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|07xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|08xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|09xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|13xxxx
|Shawn Ligocki
|Yes
|Yes
|1,192,442
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|20xxxx
|@C7X
|Yes
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/11iGTKsvu2Y7aFrwOcWS1LYvcN6i_7-JM?usp=sharing Google Drive folder]
|-
|243308
|@uni
|Yes
|No
|TBE
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|[https://discord.com/channels/960643023006490684/1369339127652159509/1373660959960469545 Discord post]
|-
|25xxxx
|@stokastic
|Yes
|No
|1,056,591
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|26xxxx
|@stokastic
|Yes
|No
|958,289
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|27xxxx
|@stokastic
|Yes
|No
|1,052,946
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|28xxxx
|@stokastic
|Yes
|No
|956,935
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|29xxxx
|@stokastic
|Yes
|No
|1,052,415
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|30xxxx
|@stokastic
|Yes
|No
|1,032,095
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|31xxxx
|@stokastic
|Yes
|No
|1,436,970
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|32xxxx
|@stokastic
|Yes
|No
|1,036,950
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|33xxxx
|@stokastic
|Yes
|No
|1,432,081
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|34xxxx
|@stokastic
|Yes
|No
|1,032,970
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|
35xxxx - 
38xxxx
|Terry Ligocki
|No
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|39xxxx
|Terry Ligocki
|Yes
|Yes
|1,093,938
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ}}
|10 ↑↑ 193
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|40xxxx
| rowspan="6" |Andrew Ducharme
|No
|No
|TBD
|TBD
|TBD
| rowspan="6" |[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|-
|41xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|42xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|43xxxx
|Yes
|Yes
|817,332
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|-
|44xxxx
|Yes
|Yes
|729,686
|{{TM|1RB1LC_1RC0RC_1RD1LA_0RE1RF_1LC0LG_1LA1LE_1RZ1LF}}
|10 ↑↑ 76.36
|-
|45xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|49xxxx
|Tobiáš Brichta
|No
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/1-csgJ5uSIX3SKlqTkSnhkUuEYLKgCw81 Google Drive folder]
|-
|500xxx
|@prurq
|Yes
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
|-
|60xxxx
|@gerbil5709
|No
|No
|TBD
|TBD
|TBD
|
|-
|69xxxx
|@poppuncher
|Yes
|No
|TBD
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|10 ↑↑ 133
|[https://drive.google.com/drive/folders/1KlCZqXxqVPuBPkDcCBocuMPA8paq9b8P?usp=drive_link Google Drive folder]
|-
|70xxxx
|@hipparcos
|No
|No
|TBD
|{{TM|1RB0LF_1LC1LE_1RE0LD_0LC0LA_1LB1RA_0LG0RC_1RZ0LA}}
|10 ↑↑ 26
|[https://discord.com/channels/960643023006490684/1369339127652159509/1372088267364634704 Posted to Discord]
|-
|75xxxx
|Terry Ligocki
|Yes
|Yes
|1,103,089
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|80xxxx
|@xnoobspeakable
|Yes
|No
|964,396
|TBD
|TBD
|[https://drive.google.com/drive/folders/1TpuEC7KottEmvsFnCREugnlVMPaY5ZHi?usp=sharing Google Drive folder]
|-
|81xxxx
|@xnoobspeakable
|No
|No
|TBD
|TBD
|TBD
|
|-
|
85xxxx - 
9xxxxx
|Terry Ligocki
|Yes
|Yes
|13,396,923
|
{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}} 
{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}} 
{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}} 
{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}} 
{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|
10 ↑↑ 286 
10 ↑↑ 193 
10 ↑↑ 188 
10 ↑↑ 117 
10 ↑↑ 113
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|}
[[Category:BB Domain]]

BB(7)

2025-06-03T08:32:38Z

Konkhra: Uni, not P. Michel

The 7-state, 2-symbol Busy Beaver problem '''BB(7)''' is a mostly unexplored domain with only preliminary information.

The current BB(7) champion is {{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}} discovered by Pavel Kropitz in 2025 proving the lower bound:<math display="block">S(7) > \Sigma(7) > 2 \uparrow^{11} 2 \uparrow^{11} 3</math>

== History ==
Before 2025, the only known BB(7) champions were produced by hand, not by search. Example, Milton Green designed a machine in 1964 that had [[sigma score]] 22,961 and Wythagoras modified a BB(6) champion in 2014 to produce a machine that had sigma score <math>> 10 \uparrow\uparrow 5</math>.

In May 2025, mxdys shared [https://github.com/ccz181078/TM C++ code] that breaks up the BB(7) enumeration into 1 million subtasks which each run for about 2 minutes and leave ~100 holdouts each. Various folks on Discord have been investigating different sections of this domain to search for champions.

== Top Halters ==
Based on limited search through a subset of the 1 million subtasks from mxdys's code, the top 20 scoring known machines are:
{| class="wikitable"
!TM
!Approximate sigma score
!Discoverer
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|Pavel Kropitz
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286.17
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
|10 ↑↑ 246.32
|@Iijil
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LG_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RG0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ0RE}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LF0RF_0RA1RE_1RZ0RA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LD0RF_0RA1RE_1RZ0RA}}
|10 ↑↑ 188.28
|@XnoobSpeakable, @Peacemaker II
|-
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|10 ↑↑ 133
|@poppuncher
|-
|{{TM|1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF}}
|10 ↑↑ 129.24
|@Iijil
|-
|{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}}
|10 ↑↑ 116.97
|Terry Ligocki
|-
|{{TM|1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG}}
|10 ↑↑ 116.05
|
|-
|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ}}
|10 ↑↑ 115.52
|@prurq
|-
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|Shawn Ligocki
|-
|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 113.37
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|Andrew Ducharme
|-
|{{TM|1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ}}
|10 ↑↑ 93.78
|Terry Ligocki
|}
The top 20 known halters with unique scores are:
{| class="wikitable"
!TM
!Approximate sigma score
!Discoverer
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|Pascal Michel
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|10 ↑↑ 286.17
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
|10 ↑↑ 246.32
|@Iijil
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|10 ↑↑ 192.67
|Terry Ligocki
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188.28
|Terry Ligocki
|-
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|10 ↑↑ 133
|@poppuncher
|-
|{{TM|1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF}}
|10 ↑↑ 129.24
|@Iijil
|-
|{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}}
|10 ↑↑ 116.97
|Terry Ligocki
|-
|{{TM|1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG}}
|10 ↑↑ 116.05
|
|-
|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ}}
|10 ↑↑ 115.52
|@prurq
|-
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|Shawn Ligocki
|-
|{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|10 ↑↑ 113.37
|Terry Ligocki
|-
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|Andrew Ducharme
|-
|{{TM|1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ}}
|10 ↑↑ 93.78
|Terry Ligocki
|-
|{{TM|1RB1LB_1LC1RE_1RD1RC_0RE0RD_1LF0RB_1LF1LG_1RZ0LA}}
|10 ↑↑ 86.40
|Terry Ligocki
|-
|{{TM|1RB1LC_1RC0LG_1RD0RG_0LE0RA_1LC0LF_0LD1LF_1RZ1RA}}
|10 ↑↑ 82.44
|Terry Ligocki
|-
|{{TM|1RB1LC_1RC0RC_1RD1LA_0RE1RF_1LC0LG_1LA1LE_1RZ1LF}}
|10 ↑↑ 76.36
|Andrew Ducharme
|-
|{{TM|1RB0LD_1RC0RF_0RD1RA_1LE0RB_0LA0LB_1RA1RG_0RA1RZ}}
|10 ↑↑ 64.03
|Terry Ligocki
|-
|{{TM|1RB1RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_1RG1RZ_0LG0LE}}
|10 ↑↑ 63.56
|Terry Ligocki
|-
|{{TM|1RB0LD_1RC0RF_0RD1RA_1LE0RB_0LA0LB_1RA1RG_1LE1RZ}}
|10 ↑↑ 61.02
|Terry Ligocki
|}

== Current Progress ==
This is a summary of the 1 million subtasks from mxdys's code that have been processed, including further processing by Shawn Ligocki's linear rule code ("TBD" = "To Be Determined", "TBE" = "To Be Entered"):
{| class="wikitable defaultleft"
!rowspan="2"|Task range
!rowspan="2"|Done by
!colspan="2"|Completed
!rowspan="2"|# holdouts
!rowspan="2"|Maximum Score TM
!rowspan="2"|~Sigma
!rowspan="2"|Source
|-
!enumeration
!linear rule
|-
|00xxxx
|@Iijil
|Yes
|Yes
|728,495
|{{TM|1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC}}
|10 ↑↑ 46
| rowspan="10" |[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD Google Drive folder]
|-
|01xxxx
|@Iijil
|Yes
|Yes
|1,056,253
|TBD
|TBD
|-
|02xxxx
|@Iijil
|Yes
|No
|963,486
|TBD
|TBD
|-
|03xxxx
|@Iijil
|Yes
|No
|1,052,504
|TBD
|TBD
|-
|04xxxx
|@Iijil
|Yes
|No
|955,711
|TBD
|TBD
|-
|05xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|06xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|07xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|08xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|09xxxx
|@Iijil
|Yes
|No
|TBD
|TBD
|TBD
|-
|13xxxx
|Shawn Ligocki
|Yes
|Yes
|1,192,442
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|10 ↑↑ 114.60
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|20xxxx
|@C7X
|Yes
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/11iGTKsvu2Y7aFrwOcWS1LYvcN6i_7-JM?usp=sharing Google Drive folder]
|-
|243308
|@uni
|Yes
|No
|TBE
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|[https://discord.com/channels/960643023006490684/1369339127652159509/1373660959960469545 Discord post]
|-
|25xxxx
|@stokastic
|Yes
|No
|1,056,591
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|26xxxx
|@stokastic
|Yes
|No
|958,289
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|27xxxx
|@stokastic
|Yes
|No
|1,052,946
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|28xxxx
|@stokastic
|Yes
|No
|956,935
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|29xxxx
|@stokastic
|Yes
|No
|1,052,415
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|30xxxx
|@stokastic
|Yes
|No
|1,032,095
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|31xxxx
|@stokastic
|Yes
|No
|1,436,970
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|32xxxx
|@stokastic
|Yes
|No
|1,036,950
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|33xxxx
|@stokastic
|Yes
|No
|1,432,081
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|34xxxx
|@stokastic
|Yes
|No
|1,032,970
|TBD
|TBD
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]
|-
|
35xxxx - 
38xxxx
|Terry Ligocki
|No
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|39xxxx
|Terry Ligocki
|Yes
|Yes
|1,093,938
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ}}
|10 ↑↑ 193
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|40xxxx
| rowspan="6" |Andrew Ducharme
|No
|No
|TBD
|TBD
|TBD
| rowspan="6" |[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|-
|41xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|42xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|43xxxx
|Yes
|Yes
|817,332
|{{TM|1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG}}
|10 ↑↑ 93.81
|-
|44xxxx
|Yes
|Yes
|729,686
|{{TM|1RB1LC_1RC0RC_1RD1LA_0RE1RF_1LC0LG_1LA1LE_1RZ1LF}}
|10 ↑↑ 76.36
|-
|45xxxx
|No
|No
|TBD
|TBD
|TBD
|-
|49xxxx
|Tobiáš Brichta
|No
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/1-csgJ5uSIX3SKlqTkSnhkUuEYLKgCw81 Google Drive folder]
|-
|500xxx
|@prurq
|Yes
|No
|TBD
|TBD
|TBD
|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
|-
|60xxxx
|@gerbil5709
|No
|No
|TBD
|TBD
|TBD
|
|-
|69xxxx
|@poppuncher
|Yes
|No
|TBD
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|10 ↑↑ 133
|[https://drive.google.com/drive/folders/1KlCZqXxqVPuBPkDcCBocuMPA8paq9b8P?usp=drive_link Google Drive folder]
|-
|70xxxx
|@hipparcos
|No
|No
|TBD
|{{TM|1RB0LF_1LC1LE_1RE0LD_0LC0LA_1LB1RA_0LG0RC_1RZ0LA}}
|10 ↑↑ 26
|[https://discord.com/channels/960643023006490684/1369339127652159509/1372088267364634704 Posted to Discord]
|-
|75xxxx
|Terry Ligocki
|Yes
|Yes
|1,103,089
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LF_0RA1RE_1RZ1LA}}
|10 ↑↑ 188
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|-
|80xxxx
|@xnoobspeakable
|Yes
|No
|964,396
|TBD
|TBD
|[https://drive.google.com/drive/folders/1TpuEC7KottEmvsFnCREugnlVMPaY5ZHi?usp=sharing Google Drive folder]
|-
|81xxxx
|@xnoobspeakable
|No
|No
|TBD
|TBD
|TBD
|
|-
|
85xxxx - 
9xxxxx
|Terry Ligocki
|Yes
|Yes
|13,396,923
|
{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}} 
{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}} 
{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}} 
{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}} 
{{TM|1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ}}
|
10 ↑↑ 286 
10 ↑↑ 193 
10 ↑↑ 188 
10 ↑↑ 117 
10 ↑↑ 113
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui Google Drive folder]
|}
[[Category:BB Domain]]

Talk:Champions

2024-12-16T06:10:30Z

Konkhra: /* Cloud search for busy beavers */

== Self-Reporting and Verification ==
This champions page has ended up with a lot of self reported and (I assume) not independently verified champions. I'm conflicted about this: On the one hand I want this wiki to have an encyclopedic/Wikipedia style: it would include things which are known, established and verified. On the other hand, I don't want to stifle innovation or gatekeep what counts as proper verification. As a compromise I have updated the table to add a "Verification" column. The idea here is to indicate which results have been independently verified by another contributor. My idea is that that verification should include some sort of write-up (wiki page, blog post, etc) describing the TM and how it is known to run this long. I have linked to examples of my own for Pavel's BB(6) and Daniel's BB(16) champions. I would love to see some independent analyses of other TMs here (especially smaller ones like Racheline's BB(14) > Graham champion). [[User:Sligocki|Sligocki]] ([[User talk:Sligocki|talk]]) 16:19, 10 December 2024 (UTC)
:Particularly interesting is Racheline's BB(14) > Graham champion. --[[User:Konkhra|Konkhra]] ([[User talk:Konkhra|talk]]) 01:53, 12 December 2024 (UTC)

==Larger champions==
What are the known two-symbol champions beyond BB(16)? Vielhaber, Chacón, and Ceballos's paper "[https://arxiv.org/abs/2303.02855v1 Friedman's 'Long Finite Sequences': The End of the Busy Beaver Contest]" gives a 2450-state two-symbol busy beaver halting after at least n(4) steps, where n is Friedman's [https://googology.miraheze.org/wiki/Block_subsequence_theorem block subsequence function], but this is a very large jump up in state count from 14 states for fω+1(65536). (This paper has some mistakes with their (symbol,state count) notation for TMs, for example referring to Aaronson's and Yedidia's machine as a (7910,2) machine rather than a (2,7910) machine, so maybe the machine whose state count I wrote here is the wrong one.) [[User:C7X|C7X]] ([[User talk:C7X|talk]]) 22:00, 17 August 2024 (UTC)

:Today i found some bounds on BB(20) and BB(21), though i'm not sure if they're new. <math>\Sigma(20) > f_{\omega+2}^2(21)</math> due to {{TM|1LR0LR_0RJ1RG_0RD1LC_1RQ1RE_1LO0RQ_1LH1LF_0LC1LH_0LI0LF_1RD0LF_---0RK_0LM1LL_0LL1LM_1LE1LN_0LF0LM_0RP1LO_0LF0RQ_1RB1RQ_0RS1LA_1LT1RS_0LP0RR|halt}} and <math>\Sigma(21) > f_{\omega^2}^2(4 \uparrow\uparrow 341)</math> due to {{TM|0LI0LF_0RJ1RG_0RD1LC_1RH1RE_1LO0RH_1LA1LF_0LC1LA_1RB1RH_1RD0LF_1LP0RK_0LM1LL_0LL1LM_1LE1LN_0RQ0LM_0RP1LO_1LR0RH_1LF1RQ_---0LS_1LH0LT_1LH1LU_0LE1LR|halt}}.
:The old googology wiki claims [https://googology.fandom.com/wiki/Busy_beaver_function#Larger_values some other bounds], two of which are already implied by the bounds mentioned above, but <math>\Sigma(85)>f_{\varepsilon_0}(1907)</math> and the bounds for more than 2 symbols seem to still be the best known.
:[[User:Racheline|Racheline]] ([[User talk:Racheline|talk]]) 23:08, 17 August 2024 (UTC)
::Racheline, congratulations on discovering a TM that crushes Graham's number. I was very impressed. but I think that in reality BB(8,2) will beat Graham's number. But it is unrealistic for a human to build such a machine. Only to search in the wild. Unfortunately. Nevertheless, congratulations again and further success!!! --[[User:Konkhra|Konkhra]] ([[User talk:Konkhra|talk]]) 03:29, 18 August 2024 (UTC)
:::And how about an article about BB(14)?--[[User:Konkhra|Konkhra]] ([[User talk:Konkhra|talk]]) 03:30, 18 August 2024 (UTC)

IMHO, beyond Graham's number I think we should only list highlights (if anything). Like first TM bigger than blah for various notable blah. Otherwise the churn on this page will be high and the quality low. But I'm open to other points of view. If we do extend this much further, I think maybe we should have a more rigorous process for getting new results demonstrated before they are added. --[[User:Sligocki|sligocki]] ([[User talk:Sligocki|talk]]) 02:57, 18 August 2024 (UTC)

Can you design very large champions as beat the <math>f_{\psi(\varepsilon_{\Omega+1})}(1000)</math>, and beat the <math>f_{\psi(\Omega_\omega)}(1000)</math>, limit for [https://googology.fandom.com/wiki/Bashicu_matrix_system BMS] or beat [https://googology.fandom.com/wiki/Loader%27s_number Loader's number]? --[[User:Jacobzheng|Jacobzheng]] ([[User talk:Jacobzheng|talk]]) 00:45, 17 September 2024 (UTC)

: Later today I can try writing one (or at least starting to write one today), but my machine would likely have thousands of states. [[User:C7X|C7X]] ([[User talk:C7X|talk]]) 15:50, 16 September 2024 (UTC)

:: I now have two-symbol machines with the following running times. In order to squeeze the best possible results out of Bashicu matrix system, some machines have a different function applied to <math>n</math> at each step (this function is what Bashicu calls the "activation function"), although at this scale it doesn't make too much of a difference.

:: {| class="wikitable"
|+ Busy Beaver lower bounds using BM4
|-
! State count !! Running time !! Activation function
|-
| 5889 || <math> >f_{\psi(\varepsilon_{\Omega+1})}(1000)</math> (using BMS to define FSes) || <math>n\mapsto n+1</math>
|-
| 5894 || <math> >f_{\psi_0(\Omega_\omega)}(1000)</math> (using BMS to define FSes) || <math>n\mapsto n+1</math>
|-
| 5908 || <math> >(0,0,0,0,0)(1,1,1,1,1)[2]</math> || <math>n\mapsto n+2</math>
|-
| 5923 || <math> >(0,0,0,0,0)(1,1,1,1,1)[5]</math> || <math>n\mapsto n+1</math>
|-
| 5941 || <math> >(0,0,0,0,0,0,0,0,0,0)(1,1,1,1,1,1,1,1,1,1)[10]</math> || <math>n\mapsto n+1</math>
|-
| 5978 || <math> >(\underbrace{0,0,\ldots,0,0}_{889})(\underbrace{1,1,\ldots,1,1}_{889})[894]</math> || <math>n\mapsto n+6</math>
|-
| 6020 || <math> >(\underbrace{0,0,\ldots,0,0}_{N})(\underbrace{1,1,\ldots,1,1}_{N})[N]</math> where <math>N</math> is <math>2^{2^{2^{2059}}}</math> || <math>n\mapsto n+5</math>
|}

:: '''Edit:''' It turns out CatIsFluffy [https://github.com/CatsAreFluffy/metamath-turing-machines beat me to it]! I don't know how many states the BMS machine has, but [https://cosearch.bbchallenge.org/contribution/m5k4ulm8 BB(1094) > Loader's number], now down to [https://github.com/CatsAreFluffy/metamath-turing-machines/commit/85948b04fc4aeb983ca6d63d6aee5ad6ef308bfe BB(1015)]. [[User:C7X|C7X]] ([[User talk:C7X|talk]]) 11:37, 4 October 2024 (UTC)

== BB(51) epsilon_0 champion ==
Can you show the transitions of BB(51) on [[Large champions transitions]] page? --[[User:Jacobzheng|Jacobzheng]] ([[User talk:Jacobzheng|talk]]) 03:24, 3 September 2024 (UTC)

: Here are the transitions and description from Racheline:
<pre>
Σ(51) > (f_ε0)^8(f_ω^ω^3(a lot)) > f_ε0+1(8)
M = (
0: ((1, -1, 0), (0, -1, 1)),
1: ((1, -1, 0), (1, 1, 2)),
2: ((1, -1, 2), (0, -1, 4)),
3: ((0, -1, 10), (1, -1, 4)),
4: ((0, -1, 3), (0, -1, 5)),
5: ((1, -1, 4), (1, 1, 6)),
6: ((1, -1, 7), (0, -1, 15)),
7: ((0, -1, 8), (1, -1, 7)),
8: ((0, -1, 9), (1, -1, 7)),
9: ((1, 1, 11), (1, -1, 9)),
10: ((0, -1, 20), (0, -1, 17)),
11: ((0, 1, 12), (1, 1, 11)),
12: ((0, 1, 13), (1, 1, 13)),
13: ((1, -1, 14), (1, 1, 12)),
14: ((0, -1, 6), (1, -1, 10)),
15: ((0, -1, 16), (1, -1, 16)),
16: ((1, -1, 20), (1, -1, 15)),
17: ((0, -1, 18), (1, -1, 18)),
18: ((1, 1, 19), (1, -1, 17)),
19: ((1, -1, 19), (1, -1, 20)),
20: ((0, -1, 50), (0, -1, 21)),
21: ((0, 1, 43), (0, -1, 9)),
22: ((0, 1, 22), (1, 1, 23)),
23: ((1, 1, 26), (0, -1, 24)),
24: ((1, -1, 25), (0, -1, 24)),
25: ((1, 1, 25), (1, 1, 22)),
26: ((0, 1, 50), (0, 1, 27)),
27: ((1, 1, 26), (1, -1, 35)),
28: ((0, 1, 29), (0, 1, 30)),
29: ((0, -1, 4), (1, 1, 28)),
30: ((1, -1, 31), (1, -1, 0)),
31: ((0, -1, 32), (1, -1, 33)),
32: ((0, -1, 33), (1, -1, 31)),
33: ((0, -1, 34), (0, -1, 35)),
34: ((0, -1, 37), (1, -1, 33)),
35: ((1, 1, 36), (1, 1, 38)),
36: ((0, 1, 37), (1, 1, 28)),
37: ((0, -1, 29), (1, 1, 36)),
38: ((1, 1, 38), (1, 1, 39)),
39: ((0, 1, 38), (1, 1, 40)),
40: ((0, 1, 41), (1, -1, 42)),
41: ((1, -1, 49), (1, 1, 40)),
42: ((1, 1, 36), (0, -1, 42)),
43: ((0, 1, 44), (1, 1, 44)),
44: ((1, -1, 45), (1, 1, 43)),
45: ((0, -1, 46), (1, -1, 46)),
46: ((0, 1, 22), (1, -1, 45)),
47: ((1, -1, 41), (1, -1, 47)),
48: ((0, -1, 47), (0, -1, 49)),
49: ((1, -1, 22), (1, -1, 48)),
50: ((0, -1, 48), (1, 1, halt))
)

(start from state 30)
</pre>

: I haven't investigated it yet. [[User:Sligocki|Sligocki]] ([[User talk:Sligocki|talk]]) 14:27, 3 September 2024 (UTC)

:: It directly simulates Address Notation, which is a different way to write Primitive Sequence System (PrSS for short, it's 1-row Bashicu Matrix System). Here are the expansion rules of Address Notation:
::: Given a sequence <math>S</math> of natural numbers, to compute its expansion, start by letting <math>c</math> be the last element of <math>S</math>. If <math>c=0</math>, then <math>S</math> is a successor and its predecessor is <math>S</math> without the last element. Otherwise, find the last element <math>r</math> of <math>S</math> which is less than <math>c</math>. Decrease <math>c</math> by <math>1</math>, and let <math>B</math> be everything in this new sequence after <math>r</math>. Append infinitely many copies of <math>B</math>.
:: Since the sequences are ordered lexicographically and each element decreases by <math>1</math> until it is <math>0</math>, for any fundamental sequence system where each <math>S[n]</math> is formed by taking an initial subsequence of the expansion of <math>S</math> and changing the last element of that subsequence to a smaller or equal natural number, the ordinal notation given by the fundamental sequence system is the same. If i remember correctly, the TM simulates a variant <math>h</math> of the Hardy Hierarchy with a fundamental sequence system where the FS of each standard <math>S</math> contains all sequences longer than <math>S</math> formed this way from its expansion (except for the first one or two).
:: Specifically,
::: <math>h_0(n)=n+c_0</math>
::: <math>h_{\alpha+1}(n)=h_\alpha(n+c_1)</math>
::: <math>h_\alpha(n)=h_{\alpha[n]}(c_2)</math> for limit <math>\alpha</math>
::: <math>h_{\varepsilon_0}(n) = h_{(0,\lfloor\frac{n+c_3}{2}\rfloor)}(c_4) = h_{\omega\uparrow\uparrow\lfloor\frac{n+c_3}{2}\rfloor}(c_4)</math>
:: for some constants <math>c_0,c_1,c_2,c_3,c_4</math> for which the hierarchy is not degenerate (the constants can be deduced easily from the TM's space-time diagram). In particular, the non-degeneracy means that for most FGHs <math>f</math> with "natural" FS systems, we will have <math>f_{\alpha+1}(n)<h_{\omega^{\alpha+1}}(n+k)</math> for some small constant <math>k</math> (depending on <math>f</math>), and as long as the FGH's FS system has <math>\varepsilon_0[n]\le\omega\uparrow\uparrow(n+c)</math> for some constant <math>c</math>, we have <math>f_{\varepsilon_0}(n)<h_{\varepsilon_0}(2(n+c)+k)</math> for some small constant <math>k</math> (also depending on <math>f</math>. For example, the Wainer Hierarchy is one of these "natural" FGHs (and one of the most well-known ones at this level), and if we extend it to include <math>f_{\varepsilon_0}</math> and <math>f_{\varepsilon_0+1}</math> with the FS <math>\varepsilon_0[n]=\omega\uparrow\uparrow n</math>, it does indeed satisfy <math>f_{\varepsilon_0}(n)<h_{\varepsilon_0}(2n+k)</math> for small <math>k</math>, which means that since the TM computes <math>h_{\varepsilon_0}^8(n)</math> for a large <math>n</math>, its output is larger than <math>f_{\varepsilon_0+1}(8)</math>. [[User:Racheline|Racheline]] ([[User talk:Racheline|talk]]) 19:06, 3 September 2024 (UTC)

I think the bbchallenge can search BB(7) and BB(4,3) in the wild. --[[User:Jacobzheng|Jacobzheng]] ([[User talk:Jacobzheng|talk]]) 14:56, 30 October 2024 (UTC)

: I have thought about writing a program that searches for Ackermann's worm-like behavior of TMs (or at least a program for exponential behavior), but I wouldn't be sure how to do it. [[User:C7X|C7X]] ([[User talk:C7X|talk]]) 22:07, 30 October 2024 (UTC)

Who can design a <math>\psi(\varepsilon_{\Omega+1})</math> level machine. --[[User:Jacobzheng|Jacobzheng]] ([[User talk:Jacobzheng|talk]]) 05:24, 8 December 2024 (UTC)

== Cloud search for busy beavers ==
We still lack a website for cloud search busy beaver functions. --[[User:Jacobzheng|Jacobzheng]] ([[User talk:Jacobzheng|talk]]) 07:07, 15 December 2024 (UTC)

: In the case of distributed computing projects like Catalogue and Great Internet Mersenne Prime Search, it seems like those are distributed to divvy up a large finite amount of computation. I don't know much about searching for Busy Beavers (e.g. if there is such a thing as an automated process for finding accelerated simulators) but would distributed finite computation be able to help reduce holdout lists? [[User:C7X|C7X]] ([[User talk:C7X|talk]]) 09:05, 15 December 2024 (UTC)

It may be able to search the busy beaver domain BB(7) or even larger more quickly. [[User:Jacobzheng|Jacobzheng]] ([[User talk:Jacobzheng|talk]]) 13:38, 15 December 2024 (UTC)

: Certainly it could do something like direct simulation quickly, but is there a known way to automate more advanced techniques to look for long-running machines? [[User:C7X|C7X]] ([[User talk:C7X|talk]]) 22:17, 15 December 2024 (UTC)
::questions like these should be asked on discord. Few people look at this page.--[[User:Konkhra|Konkhra]] ([[User talk:Konkhra|talk]]) 06:10, 16 December 2024 (UTC)

Talk:Champions

2024-12-12T01:53:31Z

Konkhra: /* Self-Reporting and Verification */

Talk:Champions

2024-08-18T03:30:40Z

Konkhra:

==Larger champions==
What are the known two-symbol champions beyond BB(16)? Vielhaber, Chacón, and Ceballos's paper "[https://arxiv.org/abs/2303.02855v1 Friedman's 'Long Finite Sequences': The End of the Busy Beaver Contest]" gives a 2450-state two-symbol busy beaver halting after at least n(4) steps, where n is Friedman's [https://googology.miraheze.org/wiki/Block_subsequence_theorem block subsequence function], but this is a very large jump up in state count from 14 states for fω+1(65536). (This paper has some mistakes with their (symbol,state count) notation for TMs, for example referring to Aaronson's and Yedidia's machine as a (7910,2) machine rather than a (2,7910) machine, so maybe the machine whose state count I wrote here is the wrong one.) [[User:C7X|C7X]] ([[User talk:C7X|talk]]) 22:00, 17 August 2024 (UTC)

:Today i found some bounds on BB(20) and BB(21), though i'm not sure if they're new. <math>\Sigma(20) > f_{\omega+2}^2(21)</math> due to {{TM|1LR0LR_0RJ1RG_0RD1LC_1RQ1RE_1LO0RQ_1LH1LF_0LC1LH_0LI0LF_1RD0LF_---0RK_0LM1LL_0LL1LM_1LE1LN_0LF0LM_0RP1LO_0LF0RQ_1RB1RQ_0RS1LA_1LT1RS_0LP0RR|halt}} and <math>\Sigma(21) > f_{\omega^2}^2(4 \uparrow\uparrow 341)</math> due to {{TM|0LI0LF_0RJ1RG_0RD1LC_1RH1RE_1LO0RH_1LA1LF_0LC1LA_1RB1RH_1RD0LF_1LP0RK_0LM1LL_0LL1LM_1LE1LN_0RQ0LM_0RP1LO_1LR0RH_1LF1RQ_---0LS_1LH0LT_1LH1LU_0LE1LR|halt}}.
:The old googology wiki claims [https://googology.fandom.com/wiki/Busy_beaver_function#Larger_values some other bounds], two of which are already implied by the bounds mentioned above, but <math>\Sigma(85)>f_{\varepsilon_0}(1907)</math> and the bounds for more than 2 symbols seem to still be the best known.
:[[User:Racheline|Racheline]] ([[User talk:Racheline|talk]]) 23:08, 17 August 2024 (UTC)
::Racheline, congratulations on discovering a TM that crushes Graham's number. I was very impressed. but I think that in reality BB(8,2) will beat Graham's number. But it is unrealistic for a human to build such a machine. Only to search in the wild. Unfortunately. Nevertheless, congratulations again and further success!!! --[[User:Konkhra|Konkhra]] ([[User talk:Konkhra|talk]]) 03:29, 18 August 2024 (UTC)
:::And how about an article about BB(14)?--[[User:Konkhra|Konkhra]] ([[User talk:Konkhra|talk]]) 03:30, 18 August 2024 (UTC)

IMHO, beyond Graham's number I think we should only list highlights (if anything). Like first TM bigger than blah for various notable blah. Otherwise the churn on this page will be high and the quality low. But I'm open to other points of view. If we do extend this much further, I think maybe we should have a more rigorous process for getting new results demonstrated before they are added. --[[User:Sligocki|sligocki]] ([[User talk:Sligocki|talk]]) 02:57, 18 August 2024 (UTC)

Talk:Champions

2024-08-18T03:29:01Z

Konkhra:

==Larger champions==
What are the known two-symbol champions beyond BB(16)? Vielhaber, Chacón, and Ceballos's paper "[https://arxiv.org/abs/2303.02855v1 Friedman's 'Long Finite Sequences': The End of the Busy Beaver Contest]" gives a 2450-state two-symbol busy beaver halting after at least n(4) steps, where n is Friedman's [https://googology.miraheze.org/wiki/Block_subsequence_theorem block subsequence function], but this is a very large jump up in state count from 14 states for fω+1(65536). (This paper has some mistakes with their (symbol,state count) notation for TMs, for example referring to Aaronson's and Yedidia's machine as a (7910,2) machine rather than a (2,7910) machine, so maybe the machine whose state count I wrote here is the wrong one.) [[User:C7X|C7X]] ([[User talk:C7X|talk]]) 22:00, 17 August 2024 (UTC)

:Today i found some bounds on BB(20) and BB(21), though i'm not sure if they're new. <math>\Sigma(20) > f_{\omega+2}^2(21)</math> due to {{TM|1LR0LR_0RJ1RG_0RD1LC_1RQ1RE_1LO0RQ_1LH1LF_0LC1LH_0LI0LF_1RD0LF_---0RK_0LM1LL_0LL1LM_1LE1LN_0LF0LM_0RP1LO_0LF0RQ_1RB1RQ_0RS1LA_1LT1RS_0LP0RR|halt}} and <math>\Sigma(21) > f_{\omega^2}^2(4 \uparrow\uparrow 341)</math> due to {{TM|0LI0LF_0RJ1RG_0RD1LC_1RH1RE_1LO0RH_1LA1LF_0LC1LA_1RB1RH_1RD0LF_1LP0RK_0LM1LL_0LL1LM_1LE1LN_0RQ0LM_0RP1LO_1LR0RH_1LF1RQ_---0LS_1LH0LT_1LH1LU_0LE1LR|halt}}.
:The old googology wiki claims [https://googology.fandom.com/wiki/Busy_beaver_function#Larger_values some other bounds], two of which are already implied by the bounds mentioned above, but <math>\Sigma(85)>f_{\varepsilon_0}(1907)</math> and the bounds for more than 2 symbols seem to still be the best known.
:[[User:Racheline|Racheline]] ([[User talk:Racheline|talk]]) 23:08, 17 August 2024 (UTC)
::Racheline, congratulations on discovering a TM that crushes Graham's number. I was very impressed. but I think that in reality BB(8,2) will beat Graham's number. But it is unrealistic for a human to build such a machine. Only to search in the wild. Unfortunately. Nevertheless, congratulations again and further success!!! --[[User:Konkhra|Konkhra]] ([[User talk:Konkhra|talk]]) 03:29, 18 August 2024 (UTC)

IMHO, beyond Graham's number I think we should only list highlights (if anything). Like first TM bigger than blah for various notable blah. Otherwise the churn on this page will be high and the quality low. But I'm open to other points of view. If we do extend this much further, I think maybe we should have a more rigorous process for getting new results demonstrated before they are added. --[[User:Sligocki|sligocki]] ([[User talk:Sligocki|talk]]) 02:57, 18 August 2024 (UTC)