BB(7): Difference between revisions

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|rowspan="2"|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
|rowspan="2"|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
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Revision as of 00:25, 8 June 2025

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 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch) discovered by Pavel Kropitz in 2025 proving the lower bound:

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 .

In May 2025, mxdys shared 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.

Within three days of the code's release, the Ligockis found three champions after applying their deciders to enumerator output. Shawn Ligocki found the first two, 1RB0RF_1LC0RE_1RD1LB_1LA1LD_0RA0LE_1RG0LB_1RZ1RB (bbch) and 1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC (bbch), with sigma scores of approximately 10 ↑↑ 22 and 10 ↑↑ 35. That evening, Terry Ligocki found 1RB0LG_1RC0RF_1LD1RZ_1LF0LE_1RA1LD_1LG1RE_0LB0LB (bbch), with sigma score ~10 ↑↑ 46. These were all outpaced by Pavel's champion.

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:

TM Approximate sigma score Discoverer
1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch) Pavel Kropitz
1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE (bbch) 10 ↑↑ 519.20 Andrew Ducharme
1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ (bbch) 10 ↑↑ 286.17 Terry Ligocki
1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD (bbch) 10 ↑↑ 246.32 @Iijil
1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG (bbch) 10 ↑↑ 192.67 Terry Ligocki
1RB1RZ_1LC0RE_0LD1LB_1RE0LG_1RF0RG_0RA0LG_1RB1LG (bbch) 10 ↑↑ 192.67 Terry Ligocki
1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RG0LG_1RB1LG (bbch) 10 ↑↑ 192.67 Terry Ligocki
1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA (bbch) 10 ↑↑ 188.28 Terry Ligocki
1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ0RE (bbch) 10 ↑↑ 188.28 Terry Ligocki
1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ1LA (bbch) 10 ↑↑ 188.28 Terry Ligocki
1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LF0RF_0RA1RE_1RZ0RA (bbch) 10 ↑↑ 188.28 Terry Ligocki
1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LD0RF_0RA1RE_1RZ0RA (bbch) 10 ↑↑ 188.28 @XnoobSpeakable, @Peacemaker II
1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG (bbch) 10 ↑↑ 133.85 @poppuncher
1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF (bbch) 10 ↑↑ 129.24 @Iijil
1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ (bbch) 10 ↑↑ 116.97 Terry Ligocki
1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG (bbch) 10 ↑↑ 116.05
1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ (bbch) 10 ↑↑ 115.52 @prurq
1RB0RF_1RC0RB_0RD0RF_1LE0LG_1LC0RD_1LA0LD_1LF1RZ (bbch) 10 ↑↑ 114.61 Andrew Ducharme
1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ (bbch) 10 ↑↑ 114.60 Shawn Ligocki
1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ (bbch) 10 ↑↑ 114.57 Andrew Ducharme
1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ (bbch) 10 ↑↑ 113.37 Terry Ligocki

The top 20 known halters with unique scores are:

TM Approximate sigma score Discoverer
1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch) Pavel Kropitz
1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE (bbch) 10 ↑↑ 519.20 Andrew Ducharme
1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ (bbch) 10 ↑↑ 286.17 Terry Ligocki
1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD (bbch) 10 ↑↑ 246.32 @Iijil
1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG (bbch) 10 ↑↑ 192.67 Terry Ligocki
1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA (bbch) 10 ↑↑ 188.28 Terry Ligocki
1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG (bbch) 10 ↑↑ 133.85 @poppuncher
1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF (bbch) 10 ↑↑ 129.24 @Iijil
1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ (bbch) 10 ↑↑ 116.97 Terry Ligocki
1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG (bbch) 10 ↑↑ 116.05
1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ (bbch) 10 ↑↑ 115.52 @prurq
1RB0RF_1RC0RB_0RD0RF_1LE0LG_1LC0RD_1LA0LD_1LF1RZ (bbch) 10 ↑↑ 114.61 Andrew Ducharme
1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ (bbch) 10 ↑↑ 114.60 Shawn Ligocki
1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ (bbch) 10 ↑↑ 114.57 Andrew Ducharme
1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ (bbch) 10 ↑↑ 113.37 Terry Ligocki
1RB1RZ_1RC1RA_1RD0RB_1LE0RC_1LF0LD_1RG0LF_1RC0LG (bbch) 10 ↑↑ 108.77 Terry Ligocki
1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG (bbch) 10 ↑↑ 93.81 Andrew Ducharme
1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ (bbch) 10 ↑↑ 93.78 Terry Ligocki
1RB1LB_1LC1RE_1RD1RC_0RE0RD_1LF0RB_1LF1LG_1RZ0LA (bbch) 10 ↑↑ 86.40 Terry Ligocki
1RB1LC_1RC0LG_1RD0RG_0LE0RA_1LC0LF_0LD1LF_1RZ1RA (bbch) 10 ↑↑ 82.44 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"):

Task range Done by Completed # holdouts Maximum Score TM ~Sigma Source
enumeration linear rule
00xxxx @Iijil Yes Yes 728,495 1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC (bbch) 10 ↑↑ 45.64 Google Drive folder
01xxxx Yes Yes 817,178 1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD (bbch) 10 ↑↑ 246.32
02xxxx Yes No 963,486 TBD TBD
03xxxx Yes No 1,052,504 TBD TBD
04xxxx Yes No 955,711 TBD TBD
05xxxx Yes No 1,056,745 TBD TBD
06xxxx Yes No 950,271 TBD TBD
07xxxx Yes No 1,053,750 TBD TBD
08xxxx Yes No 951,114 TBD TBD
09xxxx Yes No 1,052,362 TBD TBD
13xxxx Shawn Ligocki Yes Yes 1,192,442 1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ (bbch) 10 ↑↑ 114.60 Google Drive folder

20xxxx -
21xxxx

@C7X Yes No 2,013,389 TBD TBD Google Drive folder
243308 @uni Yes No TBE 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch) Discord post
25xxxx @stokastic Yes No 1,056,591 1RB1RZ_1LC0LE_0LD0LC_0RE1LB_1RF0RG_0LD1RB_1RD1RA (bbch) 10 ↑↑ 31.33 Google Drive folder
26xxxx @stokastic Yes No 958,289 1RB1RZ_0LC1RB_0LE0LD_1LE1LD_0RF0LC_0RG1RF_1RD0RA (bbch) 10 ↑↑ 36.26
27xxxx @stokastic Yes No 1,052,946 1RB0RG_1LC1LB_0RE0LD_0LC1RF_0RA1RE_0LF0LB_1RF1RZ (bbch) 10 ↑↑ 63.56
28xxxx @stokastic Yes No 956,935 TBD TBD
29xxxx @stokastic Yes No 1,052,415 TBD TBD
30xxxx @stokastic Yes No 1,032,095 TBD TBD
31xxxx @stokastic Yes No 1,436,970 TBD TBD
32xxxx @stokastic Yes No 1,036,950 TBD TBD
33xxxx @stokastic Yes No 1,432,081 TBD TBD
34xxxx @stokastic Yes No 1,032,970 TBD TBD
35xxxx Terry Ligocki Yes No 1,437,841 TBD TBD Google Drive folder
36xxxx Yes Yes 798,364 1RB1LD_0LC1LE_1RD1LB_1RD0RA_1LB0RF_0RG1RE_1RZ0RA (bbch) 10 ↑↑ 26.82
37xxxx Yes Yes 1,098,681 1RB0LA_1RC0LB_1RD0RF_1LE0RC_1LA0LD_1RC1RG_1RF1RZ (bbch) 10 ↑↑ 108.77
38xxxx Yes Yes 801,308 1RB1RZ_1RC1RA_1RD0RB_1LE0RC_1LF0LD_1RG0LF_1RC0LG (bbch) 10 ↑↑ 108.77
39xxxx Yes Yes 1,093,938 1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ (bbch) 10 ↑↑ 192.67
40xxxx Andrew Ducharme Yes Yes 730,310 1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE (bbch) 10 ↑↑ 519.20 Google Drive folder
41xxxx No No TBD TBD TBD
42xxxx No No TBD TBD TBD
43xxxx Yes Yes 817,332 1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG (bbch) 10 ↑↑ 93.81
44xxxx Yes Yes 729,686 1RB1LC_1RC0RC_1RD1LA_0RE1RF_1LC0LG_1LA1LE_1RZ1LF (bbch) 10 ↑↑ 76.36
45xxxx Yes Yes 812,973 1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ (bbch) 10 ↑↑ 114.57
49xxxx Tobiáš Brichta No No TBD TBD TBD Google Drive folder
500xxx @prurq Yes Yes 120,520 1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ (bbch) 10 ↑↑ 115.52 Google Drive folder
501xxx Yes No 96,102 TBD TBD
60xxxx @gerbil5709 Yes No 957,769 TBD TBD Google Drive folder
61xxxx Yes No 1,052,047 TBD TBD
62xxxx Yes No 959,753 TBD TBD
69xxxx @poppuncher Yes No 1,053,119 1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG (bbch) 10 ↑↑ 133.85 Google Drive folder
70xxxx @hipparcos Yes Yes 798,304

1RB0LF_1RC1LE_0RD1RA_1RE1RG_0LA1LB_1LE1RG_0RC1RZ (bbch)
1RB0LF_1LC1LE_1RE0LD_0LC0LA_1LB1RA_0LG0RC_1RZ0LA (bbch)

10 ↑↑ 33.81
10 ↑↑ 26.63

Github release
71xxxx @hipparcos No No TBD TBD TBD
75xxxx Terry Ligocki Yes Yes 1,103,089 1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LF_0RA1RE_1RZ1LA (bbch) 10 ↑↑ 188.28 Google Drive folder
80xxxx @xnoobspeakable Yes No 964,396 TBD TBD Google Drive folder
81xxxx @xnoobspeakable No No TBD TBD TBD

85xxxx -
9xxxxx

Terry Ligocki Yes Yes 13,396,923 1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ (bbch) 10 ↑↑ 286.17 Google Drive folder
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