Holdouts lists: Difference between revisions

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A '''holdout''' (or undecided machine) is a [[Turing machine]] for which it is not known whether the machine halts or not from all-0 input tape. Holdouts are the machines which [[Decider|deciders]] are unable to decide.
A '''holdout''' (or undecided machine) is a [[Turing machine]] for which it is not known whether the machine halts or not from all-0 input tape. Holdouts are the machines which [[Decider|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 [[Tree Normal Form|TNF enumeration]].


Holdout lists are often shared by contributors:
{| class="wikitable"
|+Number of holdouts
!
!2-state
!3-state
!4-state
!5-state
!6-state
!7-state
|-
!2-symbol
|0
|0
|0
|0
|1314
|18,195,192
|-
!3-symbol
|0
|4
|9,401,447
|
|
|
|-
!4-symbol
|0
|12,435,284
|
|
|
|
|-
!5-symbol
|72
|
|
|
|
|
|-
!6-symbol
|556,814
|
|
|
|
|
|}


== 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.
{| class="wikitable sortable"
{| class="wikitable sortable"
|+
|+
Line 11: Line 62:
!File
!File
!Notes
!Notes
|-
|[[BB(6)]]
|January 29th, 2026
|@mxdys
|1314
|[https://discord.com/channels/960643023006490684/1239205785913790465/1466438332677619956 BB6_holdouts_1314.txt]
|
|-
|[[BB(6)]]
|December 30th, 2025
|@mxdys
|1326
|[https://wiki.bbchallenge.org/w/images/f/f0/BB6_holdouts_1326.txt BB6_holdouts_1326.txt]
|
|-
|[[BB(6)]]
|November 22nd, 2025
|Robin Rovenszky
|Variable (1325)
|[https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Google Sheets]
|Annotated list, including links to Discord discussions, always up-to-date.
|-
|[[BB(6)]]
|December 16th, 2025
|@mxdys
|1343
|[https://wiki.bbchallenge.org/w/images/9/9a/BB6_holdouts_classified_1343.txt BB6_holdouts_1343.txt]
|
|-
|[[BB(6)]]
|November 28th, 2025
|@mxdys
|1416
|[https://wiki.bbchallenge.org/w/images/9/98/BB6_holdouts_1416.txt BB6_holdouts_1416.txt]
|
|-
|[[BB(6)]]
|November 14th, 2025
|@mxdys
|1534
|[https://wiki.bbchallenge.org/w/images/0/02/BB6_holdouts_1534.txt BB6_holdouts_1534.txt]
|
|-
|[[BB(6)]]
|October 20th, 2025
|@mxdys
|1618
|[https://wiki.bbchallenge.org/w/images/e/e3/BB6_holdouts_1618.txt BB6 holdouts 1618.txt]
|
|-
|[[BB(3,4)]]
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i October 4th, 2025]
|@tjligocki
|64,777,377
|[https://drive.google.com/file/d/1I3s3w-T4NPLn-eCdaZLPgC2Mya51pyvH/view?usp=drive_link 3x4_holdouts_64777377.txt.gz]
|Work done by [[User:XnoobSpeakable|XnoobSpeakable]] and [[User:WarpedWartWars|Lúkos]].
|-
|[[BB(7)]]
|[https://discord.com/channels/960643023006490684/1369339127652159509/1423806362072256676 October 4th, 2025]
|Andrew Ducharme
|22,721,168
|[https://drive.google.com/file/d/1xAFSPh6qAR8VxsF4QVipmdc0UpdPC1hn/view bb7_holdouts_22721168.txt.zip]
|
|-
|[[BB(2,6)]]
|[https://drive.google.com/drive/folders/1TsSpW27x3LBlu5qmk-cjzCJzgo_3ehyT September 22nd, 2025]
|@tjligocki
|873,469
|[http://2x6_holdouts_873469.txt.zip 2x6_holdouts_873469.txt.zip]
|Work done by Andrew Ducharme.
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1411308408220549140 August 30 2025]
|@mxdys
|2,592
|[[:File:BB6 holdouts 2592.txt|BB6 holdouts 2592.txt]]
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1399783936019664896 July 29 2025]
|@mxdys
|2,728
|[[:File:BB6 holdouts 2728.txt|BB6 holdouts 2728.txt]]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1259770421046411285/1355593937531961365 March 29 2025]
|@mxdys
|83
|[[:File:BB2x5 Coq holdouts 83.txt]]
|
|-
|[[BB(4,3)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1320172124509311004  December 21, 2024]
|@tjligocki
|460,916,384
|[https://drive.google.com/file/d/1hKy0TuPuI62rN95j6ZLjXgE-Pue8tRsK/view?usp=drive_link 4x3_holdouts_460916384.txt.gz]
|[https://drive.google.com/drive/folders/1HBPZ17llVE_8wCy5FvRUFQ5MJsaYXAW-?usp=drive_link Google Drive directory for 4x3 TMs]
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1310648046576730124 November 25, 2024 (@icy)]
|@tjligocki
|4,319
|[https://docs.google.com/spreadsheets/d/1grhW_0neb2I8TfceN5-v70_3W42Z2U159r9L6FhPGf8/edit?usp=sharing Spreadsheet of holdouts]
|Keeping track of BB(6) progress - informal.
|-
|[[BB(3,3)]]
|November 10, 2024
|
|6
|[[:File:3x3 holdout 6.txt|3x3 holdout 6.txt]]
|
|-
|[[BB(6)]]
|[https://discordapp.com/channels/960643023006490684/1239205785913790465/1304303803213942846 November 8, 2024]
|@mxdys
|4,408
|[[:File:BB6 holdouts 4408.txt|BB6_holdouts_4408.txt]]
|
|-
|-
|[[BB(2,6)]]
|[[BB(2,6)]]
|[November 4, 2024]
|[https://discord.com/channels/960643023006490684/960643023530762341/1303219184221683733 November 4, 2024]
|@tjligocki
|@tjligocki
|22,302,296
|22,302,296
Line 20: Line 189:
|-
|-
|[[BB(3,4)]]
|[[BB(3,4)]]
|[https://discord.com/channels/960643023006490684/960643023530762341/1302767449476694188 November 3, 2024]
|[https://discord.com/channels/960643023006490684/960643023530762341/1302767449476694188 November 3, 2024]
|@tjligocki
|@tjligocki
|434,787,751
|434,787,751
Line 46: Line 215:
|[[:File:BB6 holdouts 7296.txt]]
|[[:File:BB6 holdouts 7296.txt]]
|
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1252989316175499284 June 19, 2024]
|@mxdys
|217
|[[:File:2x5_holdouts_217.txt]]
|273 holdouts minus machines solved by CTL
|-
|-
|[[BB(2,5)]]
|[[BB(2,5)]]
Line 55: Line 231:
|-
|-
|[[BB(6)]]
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1250895665719148595 June 13th 2024]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1250895665719148595 June 13, 2024]
|@tjligocki
|@tjligocki
| 12,091
| 12,091
Line 62: Line 238:
|-
|-
|[[BB(3,3)]]
|[[BB(3,3)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1249142547217907772 June 9th 2024]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1249142547217907772 June 9, 2024]
|@Justin Blanchard
|@Justin Blanchard
|22
|22
Line 69: Line 245:
|-
|-
|BB(6)
|BB(6)
|[https://discord.com/channels/960643023006490684/1239205785913790465/1248708916381220954 June 7th 2024]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1248708916381220954 June 7, 2024]
|@mxdys
|@mxdys
|12,325
|12,325
|[[:File:BB6 holdouts 12325.txt]]
|[[:File:BB6 holdouts 12325.txt]]
|Some equivalent machines are removed.
|Some equivalent machines are removed.
|-
|[[BB(5)]]
|June 2024
|BBChallenge
|0
|
|'''BB(5) is SOLVED!'''
|-
|-
|[[BB(2,5)]]
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1242679236142170203 May 22nd 2024]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1242679236142170203 May 22, 2024]
|@Justin Blanchard
|@Justin Blanchard
|499
|499
Line 82: Line 265:
|
|
|-
|-
|[[BB(5)]]
|[[BB(3,3)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1116351783040716830 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)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1116351783040716830 June 8, 2023]
|@Iijil
|2,480
|[[:File:2023 06 08.3x3.holdouts iijil 2380.txt]]
|
|
|-
|[[BB(3,3)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1116178334620070000 June 7, 2023]
|@sligocki
|2,417
|[[:File:2023 06 07.3x3.holdouts 2417.txt]]
|
|
|0
|-
|
|[[BB(6)]]
|May 27, 2023
|@sligocki
|181,851
|[https://drive.google.com/file/d/1YNwFCN6XJeDNKxxK5KbGHOAFOdIBvDb6/view?usp=drive_link 6x2.holdouts_181851.txt.gz]
|This was posted to the BBChallenge Forum (before Discord)
|-
|[[BB(6)]]
|May 10, 2023
|@sligocki
|1,458,704
|[https://drive.google.com/file/d/14bDnBt0OwuHATFBiubc_5jub0220EyXf/view?usp=drive_link 6x2.holdouts_1458704.txt.gz]
|This was posted to the BBChallenge Forum (before Discord)
|-
|[[BB(5)]]
|[https://skelet.ludost.net/bb/nreg.html circa May 13th, 2003]
|Georgi Georgiev (Skelet)
|43
|[https://bbchallenge.org/skelet List of 43 holdouts]
|
|
|}
|}
Georgi Georgiev (Skelet) posted [https://skelet.ludost.net/bb/nreg.html a list of 43 holdouts] for BB(5) in 2003. bbchallenge.org successfully reduced the number of holdouts for BB(5) to zero in June 2024.

Latest revision as of 18:38, 15 February 2026

A holdout (or undecided machine) is a Turing machine for which it is not known whether the machine halts or not from 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 1314 18,195,192
3-symbol 0 4 9,401,447
4-symbol 0 12,435,284
5-symbol 72
6-symbol 556,814

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) January 29th, 2026 @mxdys 1314 BB6_holdouts_1314.txt
BB(6) December 30th, 2025 @mxdys 1326 BB6_holdouts_1326.txt
BB(6) November 22nd, 2025 Robin Rovenszky Variable (1325) 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(6) October 20th, 2025 @mxdys 1618 BB6 holdouts 1618.txt
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(2,6) September 22nd, 2025 @tjligocki 873,469 2x6_holdouts_873469.txt.zip Work done by Andrew Ducharme.
BB(6) August 30 2025 @mxdys 2,592 BB6 holdouts 2592.txt
BB(6) July 29 2025 @mxdys 2,728 BB6 holdouts 2728.txt
BB(2,5) March 29 2025 @mxdys 83 File:BB2x5 Coq holdouts 83.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 4,319 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 4,408 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) 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 6, 2024 @mxdys 7296 File:BB6 holdouts 7296.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(2,5) May 22, 2024 @Justin Blanchard 499 File: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
Retrieved from "https://wiki.bbchallenge.org/w/index.php?title=Holdouts_lists&oldid=6240"