BB(2,6): Difference between revisions

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The 2-state, 6-symbol Busy Beaver problem, '''BB(2,6),''' is unsolved. With cryptids like [[Hydra]] in the preceding domain [[BB(2,5)]], we know that we must solve a [[Collatz-like]] problem in order to solve BB(2,6).
The 2-state, 6-symbol Busy Beaver problem, '''BB(2,6),''' is unsolved. With cryptids like [[Hydra]] in the preceding domain [[BB(2,5)]], we know that we must solve a [[Collatz-like]] problem in order to solve BB(2,6).


The current BB(2,6) champion {{TM|1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA|halting}} was discovered by Pavel Kropitz in May 2023, proving the lower bound:<math display="block">S(2,6) > \Sigma(2,6) > 10 \uparrow \uparrow 10 \uparrow\uparrow 10^{10^{115}} > 10 \uparrow \uparrow \uparrow 3</math>
The current BB(2,6) champion {{TM|1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA|halt}} was discovered by Pavel Kropitz in May 2023, proving the lower bound:<math display="block">S(2,6) > \Sigma(2,6) > 10 \uparrow \uparrow 10 \uparrow\uparrow 10^{10^{115}} > 10 \uparrow \uparrow \uparrow 3</math>


== Top Halters ==
== Top Halters ==
Line 11: Line 11:
!Discoverer
!Discoverer
|-
|-
|{{TM|1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA|halting}}
|{{TM|1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA|halt}}
|10 ↑↑↑ 3
|10 ↑↑↑ 3
|Pavel Kropitz
|Pavel Kropitz
|-
|-
|{{TM|1RB3LA4LB0RB1RA3LA_2LA2RA4LA1RA5RB1RZ|halting}}
|{{TM|1RB3LA4LB0RB1RA3LA_2LA2RA4LA1RA5RB1RZ|halt}}
|10 ↑↑ 91  
|10 ↑↑ 91  
|Pavel Kropitz
|Pavel Kropitz
|-
|-
|{{TM|1RB2LA1RA4LA5RA0LB_1LA3RA2RB1RZ3RB4LA|halting}}
|{{TM|1RB2LA1RA4LA5RA0LB_1LA3RA2RB1RZ3RB4LA|halt}}
|10 ↑↑ 70  
|10 ↑↑ 70  
|Shawn Ligocki
|Shawn Ligocki
|-
|-
|{{TM|1RB2LB0RA2RA5RA1LB_2LA4RB3LB2RB0RB1RZ|halting}}
|{{TM|1RB2LB0RA2RA5RA1LB_2LA4RB3LB2RB0RB1RZ|halt}}
|10 ↑↑ 54.90  
|10 ↑↑ 54.90  
|Andrew Ducharme*
|Andrew Ducharme*
|-
|-
|{{TM|1RB3RB1LB5LA2LB1RZ_2LA3RA4RB2LB0LA4RB|halting}}
|{{TM|1RB3RB1LB5LA2LB1RZ_2LA3RA4RB2LB0LA4RB|halt}}
|10 ↑↑ 42.17  
|10 ↑↑ 42.17  
|Andrew Ducharme*
|Andrew Ducharme*
|-
|-
|{{TM|1RB3LB0RB5RA1LB1RZ_2LB3LA4RA0RB0RA2LB|halting}}
|{{TM|1RB3LB0RB5RA1LB1RZ_2LB3LA4RA0RB0RA2LB|halt}}
|10 ↑↑ 40.07
|10 ↑↑ 40.07
|Andrew Ducharme*
|Andrew Ducharme*
|-
|-
|{{TM|1RB3LB3RB4LA2LA4LA_2LA2RB1LB0RA5RA1RZ|halting}}
|{{TM|1RB3LB3RB4LA2LA4LA_2LA2RB1LB0RA5RA1RZ|halt}}
|10 ↑↑ 21.54
|10 ↑↑ 21.54
|Andrew Ducharme*
|Andrew Ducharme*
|-
|-
|{{TM|1RB0RA3RB0LB1RA2LA_2LA4LB1RA3LB5LB1RZ|halting}}
|{{TM|1RB2LB3LA1RA0RA1RZ_1LA2RB1LB4RB5RA3LA|halt}}
|10 ↑↑ 20.58
|Shawn Ligocki
|-
|{{TM|1RB0RA3RB0LB1RA2LA_2LA4LB1RA3LB5LB1RZ|halt}}
|10 ↑↑ 17.53
|10 ↑↑ 17.53
|Andrew Ducharme*
|Andrew Ducharme*
|-
|-
|{{TM|1RB0RA3RB0LB5LA2LA_2LA4LB1RA3LB5LB1RZ|halting}}
|{{TM|1RB0RA3RB0LB5LA2LA_2LA4LB1RA3LB5LB1RZ|halt}}
|10 ↑↑ 17.53
|10 ↑↑ 17.53
|Andrew Ducharme*
|Andrew Ducharme*
|}
All decimal places are truncated. Discoverers are asterisked where it is unclear if the TM had been found but unreported by someone previously (namely Shawn Ligocki).
== Filtering ==
Starting from Terry Ligocki's [[holdouts list]] of 22,302,296 TMs, additional filtering has been performed:
(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
|-
|-
|{{TM|1RB3RA4LA1LA0LA1RZ_2LA0LB1RA1LB5LB2RA|halting}}
!Input
|10 ↑↑ 15.49
!Output
|Andrew Ducharme*
!<math>*^3</math>
!<math>*^4</math>
|-
|style="text-align:center" |Andrew Ducharme
|22,302,296
|20,778,101
|6.8%
|274.6
|
|22.56
|style="text-align:left" |Enumerate.py with --no-sim and --lin-steps=10_000
|rowspan="7" |[https://drive.google.com/drive/folders/1TsSpW27x3LBlu5qmk-cjzCJzgo_3ehyT?usp=share_link Google Drive]
|-
|style="text-align:center" |Andrew Ducharme
|20,778,101
|19,257,876
|7.3%
|200.0
|
|28.00
|style="text-align:left" |lr_enum_continue 1M steps
|-
|style="text-align:center" |Andrew Ducharme
|19,280,508
|19,004,377
|1.4%
|2,174.6
|
|2.46
|style="text-align:left" |Enumerate.py with --block-multiple=1, max-loops=20_000, and --time=1
|-
|style="text-align:center" |Andrew Ducharme
|19,005,529
|18,952,159
|0.3%
|1,952.7
|
|2.70
|style="text-align:left" |Enumerate.py with --block-multiple=2, max-loops=20_000, and --time=120
|-
|style="text-align:center" |Andrew Ducharme
|18,952,159
|18,054,938
|4.7%
|4,168.4
|
|1.26
|style="text-align:left" |CPS_Filter with --block-size=7
|-
|style="text-align:center" |Andrew Ducharme
|18,068,066
|17,996,475
|0.4%
|1,100.0
|
|4.50
|style="text-align:left" |lr_enum_continue 10M steps
|-
|style="text-align:center" |Andrew Ducharme
|17,999,451
|17,629,828
|2.1%
|1,610.6
|
|0.31
|style="text-align:left" |Enumerate.py with --block-multiple=8, max-loops=100_000, and --time=0.45
|}
|}
All decimal places are truncated. Discoverers are asterisked where it is unclear if the TM had been found but unreported by someone previously (namely Shawn Ligocki).
 
A far more efficient pipeline would immediately apply lr_enum_continue out to 1M steps to Terry Ligocki's holdout list. lr_enum_continue, written in C++, is about 400x faster than Enumerate.py at checking for Lin Recursion. Using Enumerate.py meant its Reverse Engineering decider was applied to all holdouts, and solved 74,089 TMs (0.33% of holdouts)...at the cost of roughly 274.1 hours of compute.
 
 
[[Category: BB Domains]]

Revision as of 05:11, 9 September 2025

The 2-state, 6-symbol Busy Beaver problem, BB(2,6), is unsolved. With cryptids like Hydra in the preceding domain BB(2,5), we know that we must solve a Collatz-like problem in order to solve BB(2,6).

The current BB(2,6) champion 1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch) was discovered by Pavel Kropitz in May 2023, proving the lower bound:

Top Halters

The highest known scoring machines are:

TM Approximate sigma score Discoverer
1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch) 10 ↑↑↑ 3 Pavel Kropitz
1RB3LA4LB0RB1RA3LA_2LA2RA4LA1RA5RB1RZ (bbch) 10 ↑↑ 91 Pavel Kropitz
1RB2LA1RA4LA5RA0LB_1LA3RA2RB1RZ3RB4LA (bbch) 10 ↑↑ 70 Shawn Ligocki
1RB2LB0RA2RA5RA1LB_2LA4RB3LB2RB0RB1RZ (bbch) 10 ↑↑ 54.90 Andrew Ducharme*
1RB3RB1LB5LA2LB1RZ_2LA3RA4RB2LB0LA4RB (bbch) 10 ↑↑ 42.17 Andrew Ducharme*
1RB3LB0RB5RA1LB1RZ_2LB3LA4RA0RB0RA2LB (bbch) 10 ↑↑ 40.07 Andrew Ducharme*
1RB3LB3RB4LA2LA4LA_2LA2RB1LB0RA5RA1RZ (bbch) 10 ↑↑ 21.54 Andrew Ducharme*
1RB2LB3LA1RA0RA1RZ_1LA2RB1LB4RB5RA3LA (bbch) 10 ↑↑ 20.58 Shawn Ligocki
1RB0RA3RB0LB1RA2LA_2LA4LB1RA3LB5LB1RZ (bbch) 10 ↑↑ 17.53 Andrew Ducharme*
1RB0RA3RB0LB5LA2LA_2LA4LB1RA3LB5LB1RZ (bbch) 10 ↑↑ 17.53 Andrew Ducharme*

All decimal places are truncated. Discoverers are asterisked where it is unclear if the TM had been found but unreported by someone previously (namely Shawn Ligocki).

Filtering

Starting from Terry Ligocki's holdouts list of 22,302,296 TMs, additional filtering has been performed:

(done to reduce column size: = % Reduced, = Compute Time (core-hours), = Decided, = Processed)

Done by Holdout TMs TMs/sec/core Description Data
Input Output
Andrew Ducharme 22,302,296 20,778,101 6.8% 274.6 22.56 Enumerate.py with --no-sim and --lin-steps=10_000 Google Drive
Andrew Ducharme 20,778,101 19,257,876 7.3% 200.0 28.00 lr_enum_continue 1M steps
Andrew Ducharme 19,280,508 19,004,377 1.4% 2,174.6 2.46 Enumerate.py with --block-multiple=1, max-loops=20_000, and --time=1
Andrew Ducharme 19,005,529 18,952,159 0.3% 1,952.7 2.70 Enumerate.py with --block-multiple=2, max-loops=20_000, and --time=120
Andrew Ducharme 18,952,159 18,054,938 4.7% 4,168.4 1.26 CPS_Filter with --block-size=7
Andrew Ducharme 18,068,066 17,996,475 0.4% 1,100.0 4.50 lr_enum_continue 10M steps
Andrew Ducharme 17,999,451 17,629,828 2.1% 1,610.6 0.31 Enumerate.py with --block-multiple=8, max-loops=100_000, and --time=0.45

A far more efficient pipeline would immediately apply lr_enum_continue out to 1M steps to Terry Ligocki's holdout list. lr_enum_continue, written in C++, is about 400x faster than Enumerate.py at checking for Lin Recursion. Using Enumerate.py meant its Reverse Engineering decider was applied to all holdouts, and solved 74,089 TMs (0.33% of holdouts)...at the cost of roughly 274.1 hours of compute.

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