BB(2,6): Difference between revisions

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(→‎Top Halters: Added Template:incomplete list)
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|10 ↑↑ 17.53
|10 ↑↑ 17.53
|Shawn Ligocki
|Shawn Ligocki
|}
|-
|{{TM|1RB0RA3RB0LB5LA2LA_2LA4LB1RA3LB5LB1RZ}|halt}}
|10 ↑↑ 17.53
|Andrew Ducharme
|}
|-
|{{TM|1RB3RA4LB5RA5LB4RA_2LA1RZ1RB2LA5LA0LA}|halt}}
|10 ↑↑ 17.08
|Andrew Ducharme
|}
|-
|{{TM|1RB3RA4LA1LA0LA1RZ_2LA0LB1RA1LB5LB2RA}|halt}}
|10 ↑↑ 15.44
|Andrew Ducharme
|}
|-
|{{TM|1RB3RB5LA1LA2RA3LA_2LA3RA2LB4LB1RZ2LA}|halt}}
|10 ↑↑ 14.35
|Andrew Ducharme
|}
|-
|{{TM|1RB3RB5LA1LA2RA3LA_2LA3RA2LB4LB1RZ3RA}|halt}}
|10 ↑↑ 14.17
|Andrew Ducharme
|}
|-
|{{TM|1RB3RB5LA1LA2RA3LA_2LA3RA2LB4LB1RZ1LA}|halt}}
|10 ↑↑ 14.05
|Andrew Ducharme
|}
|-
|{{TM|1RB3RB5LA1LA2RA3LA_2LA3RA2LB4LB1RZ0RA}|halt}}
|10 ↑↑ 13.69
|Andrew Ducharme
|}
|-
|{{TM|1RB3LA3RA4LB2LB0LA_2LA5LB2RB0RA0RA1RZ}|halt}}
|10 ↑↑ 12.42
|Andrew Ducharme
|}
|-
|{{TM|1RB0LB4LA2RA2RB1LB_2LA4LA3LB5LA1RA1RZ}|halt}}
|10 ↑↑ 11.70
|Andrew Ducharme
|}
|-
|{{TM|1RB2LA1RA1RA5LB1RZ_1LA4RB3RB4LB0RB0RA}|halt}}
|10 ↑↑ 10.39
|Andrew Ducharme
|}
|}
All decimal places are truncated.
All decimal places are truncated.

Revision as of 10:18, 28 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 scores are given using Knuth's up-arrow notation with an extension to decimal tetration[1]. The highest known scoring machines are:

TM Approximate sigma score Discoverer
1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch) 10 ↑↑↑ 3 Pavel Kropitz
1RB3LA4LB0RB1RA3LA_2LA2RA4LA1RA5RB1RZ (bbch) 10 ↑↑ 91.17 Pavel Kropitz
1RB2LA1RA4LA5RA0LB_1LA3RA2RB1RZ3RB4LA (bbch) 10 ↑↑ 70.27 Shawn Ligocki
1RB2LB1RZ3LA2LA4RB_1LA3RB4RB1LB5LB0RA (bbch) 10 ↑↑ 69.68 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 Shawn Ligocki
1RB2LB3LA1RA0RA1RZ_1LA2RB1LB4RB5RA3LA (bbch) 10 ↑↑ 20.58 Shawn Ligocki
1RB0RA3RB0LB1RA2LA_2LA4LB1RA3LB5LB1RZ (bbch) 10 ↑↑ 17.53 Shawn Ligocki

|- |1RB0RA3RB0LB5LA2LA_2LA4LB1RA3LB5LB1RZ} (bbch) |10 ↑↑ 17.53 |Andrew Ducharme |} |- |1RB3RA4LB5RA5LB4RA_2LA1RZ1RB2LA5LA0LA} (bbch) |10 ↑↑ 17.08 |Andrew Ducharme |} |- |1RB3RA4LA1LA0LA1RZ_2LA0LB1RA1LB5LB2RA} (bbch) |10 ↑↑ 15.44 |Andrew Ducharme |} |- |1RB3RB5LA1LA2RA3LA_2LA3RA2LB4LB1RZ2LA} (bbch) |10 ↑↑ 14.35 |Andrew Ducharme |} |- |1RB3RB5LA1LA2RA3LA_2LA3RA2LB4LB1RZ3RA} (bbch) |10 ↑↑ 14.17 |Andrew Ducharme |} |- |1RB3RB5LA1LA2RA3LA_2LA3RA2LB4LB1RZ1LA} (bbch) |10 ↑↑ 14.05 |Andrew Ducharme |} |- |1RB3RB5LA1LA2RA3LA_2LA3RA2LB4LB1RZ0RA} (bbch) |10 ↑↑ 13.69 |Andrew Ducharme |} |- |1RB3LA3RA4LB2LB0LA_2LA5LB2RB0RA0RA1RZ} (bbch) |10 ↑↑ 12.42 |Andrew Ducharme |} |- |1RB0LB4LA2RA2RB1LB_2LA4LA3LB5LA1RA1RZ} (bbch) |10 ↑↑ 11.70 |Andrew Ducharme |} |- |1RB2LA1RA1RA5LB1RZ_1LA4RB3RB4LB0RB0RA} (bbch) |10 ↑↑ 10.39 |Andrew Ducharme |} All decimal places are truncated.

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
Terry Ligocki 22,302,296 20,246,662 9.2% 23.0 24.80 269.09 MitM_CTL RWL_mod sim 1001 maxT 3000 H 6 mod 2 n 6 run Google Drive
Terry Ligocki 20,246,662 19,134,631 5.5% 83.4 3.71 67.46 MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 2 n 8 run
Terry Ligocki 19,134,631 5,443,318 71.6% 46.6 81.69 114.17 chr_LRUH 20 chr_H 12 MitM_CTL NG maxT 10000 NG_n 3 run
Terry Ligocki 5,443,318 3,400,118 37.5% 16.3 34.87 92.90 chr_LRUH 8 chr_H 4 MitM_CTL NG maxT 10000 NG_n 3 run
Terry Ligocki 3,400,118 3,303,416 2.8% 14.1 1.90 66.82 MitM_CTL RWL_mod sim 1001 maxT 10000 H 8 mod 3 n 6 run
Terry Ligocki 3,303,416 3,249,427 1.6% 16.5 0.91 55.59 chr_LRUH 0 chr_H 0 MitM_CTL NG maxT 30000 NG_n 7 run
Terry Ligocki 3,249,427 3,155,741 2.9% 13.4 1.94 67.25 MitM_CTL RWL_mod sim 1001 maxT 10000 H 6 mod 2 n 6 run
Terry Ligocki 3,155,741 2,246,891 28.8% 14.1 17.93 62.24 chr_LRUH 8 chr_H 8 MitM_CTL NG maxT 30000 NG_n 2 run
Terry Ligocki 2,246,891 2,143,803 4.6% 7.5 3.82 83.19 MitM_CTL RWL_mod sim 1001 maxT 10000 H 3 mod 3 n 1 run
Terry Ligocki 2,143,803 1,938,663 9.6% 7.5 7.58 79.21 MitM_CTL CPS_LRU sim 1001 maxT 10000 LRUH 8 H 1 tH 1 n 4 run
Terry Ligocki 1,938,663 1,885,153 2.8% 7.5 1.98 71.72 chr_LRUH 14 chr_H 12 MitM_CTL NG maxT 10000 NG_n 2 run
Terry Ligocki 1,885,153 1,848,887 1.9% 10.5 0.96 49.68 MitM_CTL RWL_mod sim 1001 maxT 10000 H 3 mod 1 n 12 run
Terry Ligocki 1,848,887 1,816,027 1.8% 7.6 1.20 67.77 chr_LRUH 18 chr_H 8 MitM_CTL NG maxT 10000 NG_n 5 run
Terry Ligocki 1,816,027 1,688,951 7.0% 10.4 3.40 48.66 MitM_CTL CPS_LRU sim 1001 maxT 30000 LRUH 4 H 2 tH 0 n 2 run

References

  1. ↑ Shawn Ligocki. 2022. "Extending Up-arrow Notation"
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