Holdouts lists: Difference between revisions

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→Downloadable Holdouts Lists: added two missing BB(2,6) holdouts lists
 
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|1161
|1104
|18,036,852
|17,823,260
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!3-symbol
!3-symbol
|0
|0
|4
|4
|9,401,447
|5,641,006
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!5-symbol
!5-symbol
|69
|66
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!6-symbol
!6-symbol
|545,005
|536,112
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!File
!File
!Notes
!Notes
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1499000732236382358 April 29th, 2026]
|@mxdys
|1104
|[https://wiki.bbchallenge.org/w/images/b/bf/BB6_holdouts_1104.txt BB6_holdouts_1104.txt]
|More reduction by equivalences
|-
|[[BB(4,3)]]
|[https://drive.google.com/drive/folders/1HBPZ17llVE_8wCy5FvRUFQ5MJsaYXAW- April 26th, 2026]
|@Andrew Ducharme
|5,641,006
|[https://drive.google.com/file/d/1z8oBXUECL5dpUNAIqik2z_yI5JGmW79t/view 4x3_holdouts_5641006.txt.zip]
|Work done by Andrew Ducharme
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1497651809773289552 April 25th, 2026]
|@mxdys
|1119
|[https://wiki.bbchallenge.org/w/images/a/ab/BB6_holdouts_1119.txt BB6_holdouts_1119.txt]
|Reduction by equivalences, one halting TM
|-
|-
|[[BB(6)]]
|[[BB(6)]]
Line 138: Line 159:
|9,401,447
|9,401,447
|[https://drive.google.com/file/d/1r99v3dcdNTgGkmaydLKiZCp5KD3jGWeE/view 4x3_holdouts_9401447.txt.gz]
|[https://drive.google.com/file/d/1r99v3dcdNTgGkmaydLKiZCp5KD3jGWeE/view 4x3_holdouts_9401447.txt.gz]
|
|-
|[[BB(7)]]
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui October 25th, 2025]
|
|20,405,295
|[https://drive.google.com/file/d/12riXHC3Vz4tk_5mMV7__gZsF7hqAsZ_S/view bb7_holdouts_20405295.txt.gz]
|
|
|-
|-
Line 181: Line 209:
|[https://discord.com/channels/960643023006490684/1239205785913790465/1419290767767240734 BB6_holdouts_1691.txt]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1419290767767240734 BB6_holdouts_1691.txt]
|
|
|-
|[[BB(2,6)]]
|[https://drive.google.com/drive/folders/1TsSpW27x3LBlu5qmk-cjzCJzgo_3ehyT September 16, 2025]
|
|970,101
|[https://drive.google.com/file/d/1Vjm3Qf-4a-Zr-E3EocjPWI5bjqH2YGil/view 2x6_holdouts_970101.txt.gz]
|Work done by Terry Ligocki
|-
|[[BB(2,6)]]
|[https://drive.google.com/drive/folders/1TsSpW27x3LBlu5qmk-cjzCJzgo_3ehyT September 12, 2025]
|
|20,358,011
|[https://drive.google.com/file/d/1YOoh4Zh2Jn5zaq9-C638S6VR_4jzd6pa/view 2x6_holdouts_20358011.zip]
|Work done by Andrew Ducharme
|-
|-
|[[BB(6)]]
|[[BB(6)]]
Line 439: Line 481:
|[https://discord.com/channels/960643023006490684/1239205785913790465/1239628496184279080 BB6_holdouts_35788.txt]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1239628496184279080 BB6_holdouts_35788.txt]
|C++ version of the deciders from [[Coq-BB5]] ran on Shawns 181,851 holdouts<ref>https://discord.com/channels/960643023006490684/1239205785913790465/1239275863699361813</ref>
|C++ version of the deciders from [[Coq-BB5]] ran on Shawns 181,851 holdouts<ref>https://discord.com/channels/960643023006490684/1239205785913790465/1239275863699361813</ref>
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1233154495635259543 April 25, 2024]
|@Justin Blanchard
|920
|[https://discord.com/channels/960643023006490684/1084047886494470185/1233154495635259543 2x5.todo.txt]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1232667326126489710 April 24, 2024]
|@Justin Blanchard
|1045
|[https://discord.com/channels/960643023006490684/1084047886494470185/1232667326126489710 2x5.todo.txt]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1231941302975987844 April 22, 2024]
|@Justin Blanchard
|1588
|[https://discord.com/channels/960643023006490684/1084047886494470185/1231941302975987844 2x5.todo.txt]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1230737657076650066 April 19, 2024]
|@Justin Blanchard
|1835
|[https://discord.com/channels/960643023006490684/1084047886494470185/1230737657076650066 2x5.todo.txt]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1230491507287523409 April 18, 2024]
|@Justin Blanchard
|1921
|[https://discord.com/channels/960643023006490684/1084047886494470185/1230491507287523409 2x5.todo.txt]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1230132897583857756 April 17, 2024]
|@Justin Blanchard
|2354
|[https://discord.com/channels/960643023006490684/1084047886494470185/1230132897583857756 2x5.todo.txt]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1229770471898087506 April 16, 2024]
|@Justin Blanchard
|2438
|[https://discord.com/channels/960643023006490684/1084047886494470185/1229770471898087506 2x5.todo.txt]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1229406059274305546 April 15, 2024]
|@Justin Blanchard
|2564
|[https://discord.com/channels/960643023006490684/1084047886494470185/1229406059274305546 2x5.todo.txt]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1228351493745152083 April 12, 2024]
|@Justin Blanchard
|3364
|[https://discord.com/channels/960643023006490684/1084047886494470185/1228351493745152083 2x5.todo.txt]
|
|-
|-
|[[BB(3,3)]]
|[[BB(3,3)]]
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!File
!File
!Notes
!Notes
|-
|BBλ(39)
|[https://discord.com/channels/960643023006490684/1355653587824283678/1492187654429868062 April 10, 2026]
|@Sligocki
|Variable (49)
|[https://docs.google.com/spreadsheets/d/1jZ6TK9m3xmXUlC69727T-8WwvhALcsp8FrK6DzgThtw/edit?gid=1717120706#gid=1717120706 Spreadsheet]
|
|-
|-
|BBλ(38)
|BBλ(38)
|[https://discord.com/channels/960643023006490684/1355653587824283678/1362975027154129056 April 19, 2025]
|[https://discord.com/channels/960643023006490684/1355653587824283678/1362975027154129056 April 19, 2025]
|@Sligocki (tab)
|@Sligocki
|Variable (26)
|0
|[https://docs.google.com/spreadsheets/d/1jZ6TK9m3xmXUlC69727T-8WwvhALcsp8FrK6DzgThtw/edit?gid=563816005#gid=563816005 Spreadsheet]
|[https://docs.google.com/spreadsheets/d/1jZ6TK9m3xmXUlC69727T-8WwvhALcsp8FrK6DzgThtw/edit?gid=563816005#gid=563816005 Spreadsheet]
|
|'''BBλ(38) was solved on April 13th, 2026'''
|-
|-
|BBλ(37)
|BBλ(37)

Latest revision as of 17:51, 29 April 2026

A holdout (or undecided machine) is a Turing machine for which it is not known whether the machine halts or not from an all-0 input tape. Holdouts are the machines which deciders are yet unable to decide. Contributors have shared lists of holdouts. Some lists exclude known equivalent machines, i.e., machines whose halting status is implied by the halting status of another machine. If a holdout machine with more than one undefined transitions is found to reach a undefined transition, the number of holdouts may increase as a consequence of TNF enumeration.

Number of holdouts
2-state 3-state 4-state 5-state 6-state 7-state
2-symbol 0 0 0 0 1104 17,823,260
3-symbol 0 4 5,641,006
4-symbol 0 12,435,284
5-symbol 66
6-symbol 536,112

Downloadable Holdouts Lists

This is a 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.

BB space Date Shared by Number of holdouts File Notes
BB(6) April 29th, 2026 @mxdys 1104 BB6_holdouts_1104.txt More reduction by equivalences
BB(4,3) April 26th, 2026 @Andrew Ducharme 5,641,006 4x3_holdouts_5641006.txt.zip Work done by Andrew Ducharme
BB(6) April 25th, 2026 @mxdys 1119 BB6_holdouts_1119.txt Reduction by equivalences, one halting TM
BB(6) March 25th, 2026 @mxdys 1161 BB6_holdouts_1161.txt
BB(6) February 28th, 2026 @mxdys 1214 BB6_holdouts_1214.txt
BB(6) February 19th, 2026 @mxdys 1226 BB6_holdouts_1226.txt
BB(6) January 29th, 2026 @mxdys 1314 BB6_holdouts_1314.txt
BB(3,4) December 31st, 2025 12,435,284 3x4st10c_holdouts_12435284.txt Work done by XnoobSpeakable and Lúkos.
BB(6) December 30th, 2025 @mxdys 1326 BB6_holdouts_1326.txt
BB(6) November 22nd, 2025 Robin Rovenszky Variable Google Sheets Annotated list, including links to Discord discussions, always up-to-date.
BB(6) December 16th, 2025 @mxdys 1343 BB6_holdouts_1343.txt
BB(6) November 28th, 2025 @mxdys 1416 BB6_holdouts_1416.txt
BB(6) November 14th, 2025 @mxdys 1534 BB6_holdouts_1534.txt
BB(4,3) October 26th, 2025 9,401,447 4x3_holdouts_9401447.txt.gz
BB(7) October 25th, 2025 20,405,295 bb7_holdouts_20405295.txt.gz
BB(6) October 20th, 2025 @mxdys 1618 BB6 holdouts 1618.txt
BB(4,3) October 20th, 2025 @tjligocki 18,138,027 4x3_holdouts_18138027.txt.gz
BB(2,6) October 6th, 2025 @tjligocki 870,085 2x6_holdouts_870085.txt.zip Work done by Andrew Ducharme.
BB(3,4) October 4th, 2025 @tjligocki 64,777,377 3x4_holdouts_64777377.txt.gz Work done by XnoobSpeakable and Lúkos.
BB(7) October 4th, 2025 Andrew Ducharme 22,721,168 bb7_holdouts_22721168.txt.zip
BB(6) September 21, 2025 @mxdys 1691 BB6_holdouts_1691.txt
BB(2,6) September 16, 2025 970,101 2x6_holdouts_970101.txt.gz Work done by Terry Ligocki
BB(2,6) September 12, 2025 20,358,011 2x6_holdouts_20358011.zip Work done by Andrew Ducharme
BB(6) August 30 2025 @mxdys 2592 BB6 holdouts 2592.txt
BB(6) July 29 2025 @mxdys 2728 BB6 holdouts 2728.txt
BB(6) July 13, 2025 @mxdys 2891 BB6_holdouts_2891.txt
BB(6) July 5, 2025 @mxdys 3094 BB6_holdouts_3094.txt
BB(6) June 18, 2025 @mxdys 3335 BB6_holdouts_3335.txt
BB(2,5) March 29 2025 @mxdys 83 File:BB2x5 Coq holdouts 83.txt
BB(6) March 1, 2025 @mxdys 3571 BB6_holdouts_3571.txt
BB(4,3) December 21, 2024 @tjligocki 460,916,384 4x3_holdouts_460916384.txt.gz Google Drive directory for 4x3 TMs
BB(6) November 25, 2024 (@icy) @tjligocki 4319 Spreadsheet of holdouts Keeping track of BB(6) progress - informal.
BB(3,3) November 10, 2024 6 3x3 holdout 6.txt
BB(6) November 8, 2024 @mxdys 4408 BB6_holdouts_4408.txt
BB(2,6) November 4, 2024 @tjligocki 22,302,296 2x6_holdouts_22302296.txt.gz Google Drive directory for 2x6 TMs
BB(3,4) November 3, 2024 @tjligocki 434,787,751 3x4_holdouts_434787751.txt.gz Google Drive directory for 3x4 TMs
BB(6) October 19, 2024 @mxdys 4521 BB6_holdouts_4521.txt
BB(6) September 23, 2024 @mxdys 4741 BB6_holdouts_4741.txt
BB(6) September 7, 2024 @mxdys 4986 BB6_holdouts_4986.txt
BB(6) September 2, 2024 @mxdys 5394 File:BB6 holdouts 5394.txt
BB(6) August 4, 2024 @mxdys 5877 File:BB6 holdouts 5877.txt
BB(6) July 28, 2024 @mxdys 6417 BB6_holdouts_6417.txt
BB(6) July 15, 2024 @mxdys 7013 BB6_holdouts_7013.txt
BB(6) July 14, 2024 @Justin Blanchard 7255 BB6_holdouts_7255.txt Work done by Justin Blanchard
BB(6) July 6, 2024 @mxdys 7296 File:BB6 holdouts 7296.txt
BB(6) July 6, 2024 @Justin Blanchard 7430 BB6_holdouts_7430.txt Work done by Justin Blanchard
BB(6) July 5, 2024 @mxdys 7449 BB6_holdouts_7449.txt
BB(6) June 28, 2024 @mxdys 9366 BB6_holdouts_9366.txt
BB(6) June 24, 2024 @Justin Blanchard 9853 BB6_holdouts_9853.txt
BB(6) June 21, 2024 @mxdys 10,020 BB6_holdouts_10020.txt Work done by Justin Blanchard
BB(6) June 20, 2024 @mxdys 10,944 BB6_holdouts_10944.txt
BB(2,5) 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) June 13, 2024 @tjligocki 12,091 File:BB6 holdouts 12091.txt Work done with @Shawn Ligocki
BB(3,3) June 9, 2024 @Justin Blanchard 22 File:3x3.todo.txt, File:Mugshots small.pdf
BB(6) 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(6) May 28, 2024 @mxdys 18,560 BB6_holdouts_18560.txt
BB(2,5) May 22, 2024 @Justin Blanchard 499 File:2x5.todo.txt
BB(6) May 13, 2024 @mxdys 35,788 BB6_holdouts_35788.txt C++ version of the deciders from Coq-BB5 ran on Shawns 181,851 holdouts[1]
BB(2,5) April 25, 2024 @Justin Blanchard 920 2x5.todo.txt
BB(2,5) April 24, 2024 @Justin Blanchard 1045 2x5.todo.txt
BB(2,5) April 22, 2024 @Justin Blanchard 1588 2x5.todo.txt
BB(2,5) April 19, 2024 @Justin Blanchard 1835 2x5.todo.txt
BB(2,5) April 18, 2024 @Justin Blanchard 1921 2x5.todo.txt
BB(2,5) April 17, 2024 @Justin Blanchard 2354 2x5.todo.txt
BB(2,5) April 16, 2024 @Justin Blanchard 2438 2x5.todo.txt
BB(2,5) April 15, 2024 @Justin Blanchard 2564 2x5.todo.txt
BB(2,5) April 12, 2024 @Justin Blanchard 3364 2x5.todo.txt
BB(3,3) 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) June 8, 2023 @Iijil 2,480 File:2023 06 08.3x3.holdouts iijil 2380.txt
BB(3,3) June 7, 2023 @sligocki 2,417 File:2023 06 07.3x3.holdouts 2417.txt
BB(6) May 27, 2023 @sligocki 181,851 6x2.holdouts_181851.txt.gz This was posted to the BBChallenge Forum (before Discord)
BB(6) May 10, 2023 @sligocki 1,458,704 6x2.holdouts_1458704.txt.gz This was posted to the BBChallenge Forum (before Discord)
BB(5) circa May 13th, 2003 Georgi Georgiev (Skelet) 43 List of 43 holdouts

Busy Beaver adjacent holdouts lists

Beeping Busy Beaver

Domain Date Shared by Number of holdouts File Notes
BBB(4) June 26, 2025 @mxdys 3713 BBB4_holdouts_3713.txt

Reversible Turing machines

Domain Date Shared by Number of holdouts File Notes
BBrev(6) July 31, 2025 @Sligocki 388 BBrev6_holdouts_388.txt
BBrev(6) July 31, 2025 @Sligocki 409 BBrev6_holdouts_409.txt

Instruction-limited Busy Beaver

Domain Date Shared by Number of holdouts File Notes
BBi(8) October 7, 2025 @Shawn Ligocki 348 bbi8_holdouts_348.txt
BBi(8) October 6, 2025 @Peacemaker II 441 BBi8_holdouts_441.txt

Fractran

Domain Date Shared by Number of holdouts File Notes
BBf(22) January 25, 2026 @-d 2003 sz22_2003_unofficial.txt Result of the beeping permutation decider being run on sz22_5682.txt
BBf(21) January 25, 2026 @-d 140 sz21_140_unofficial.txt Result of the beeping permutation decider being run on sz21_345.txt
BBf(21) January 22, 2026 @-d 143 sz21_143_workinprogress.txt
BBf(22) January 2, 2026 @-d 5682 sz22_5682.txt
BBf(21) January 2, 2026 @-d 345 sz21_345.txt
BBf(21) December 15, 2025 @Sligocki 394 sz21_394.txt
BBf(20) December 15, 2025 @Sligocki 6 sz20_6.txt BBf(20) has since been solved
BBf(22) December 13, 2025 @Sligocki 10441 sz22_10441.txt 17 known halters are removed
BBf(22) December 11, 2025 @Sligocki 10458 sz22_10457.txt Known halters are removed
BBf(22) December 11, 2025 @dyuan01 11130 message.txt
BBf(22) December 10, 2025 @-d 91123 sz22_91123.txt Initial enumeration
BBf(21) November 17, 2025 @Sligocki 760 sz21_760.txt 23 halting machines are removed
BBf(21) November 16, 2025 @dyuan01 783 message.txt
BBf(20) November 13, 2025 @dyuan01 279 message.txt
BBf(20) November 13, 2025 @-d 902 sz20_902.txt

Terminating Turmites

Domain Date Shared by Number of holdouts File Notes
TT(2,4) August 1, 2025 @creeperman7002 2298 holdout_2x4_2298.txt
TT(4) July 12, 2025 @creeperman7002 99 holdout4x2.txt

Busy Beaver for Lambda Calculus

Domain Date Shared by Number of holdouts File Notes
BBλ(39) April 10, 2026 @Sligocki Variable (49) Spreadsheet
BBλ(38) April 19, 2025 @Sligocki 0 Spreadsheet BBλ(38) was solved on April 13th, 2026
BBλ(37) March 27, 2025 @Racheline 92 BBλ(37) 92 holdouts progress BBλ(37) has since been solved
BBλ(37) March 26, 2025 @Racheline 216 BBL(37)_216.txt
BBλ(37) March 26, 2025 @Racheline 278 BBL2(37)_278.txt
BBλ(37) March 26, 2025 @Sam 317 BBL2(37)_317.txt
BBλ(37) March 26, 2025 @Sam 333 BBL(37).txt

References

  1. ↑ https://discord.com/channels/960643023006490684/1239205785913790465/1239275863699361813
Retrieved from "https://wiki.bbchallenge.org/w/index.php?title=Holdouts_lists&oldid=7345"