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 unable to decide.


Holdout lists are often shared by contributors. Here is a table that summarises the number of holdout per busy beaver domain:
Holdout lists are often shared by contributors. There is a [[#Downloadable Holdout Lists|Downloadable Holdout Lists]] 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.
 
The table with the "Number of holdouts" is based on the holdout lists listed in the table below it. Thus, some of these numbers have not been independently verified. All the zero entries (no remaining holdouts) have been verified.
 
{| class="wikitable"
{| class="wikitable"
|+Number of holdouts
|+Number of holdouts
Line 10: Line 13:
!5-state
!5-state
!6-state
!6-state
!7-state
|-
|-
!2-symbol
!2-symbol
Line 16: Line 20:
|0
|0
|0
|0
|4408
|2,728
|85,853,789
|-
|-
!3-symbol
!3-symbol
|0
|0
|6
|6
|460,916,384
|
|
|
|
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|0
|0
|434,787,751
|434,787,751
|
|
|
|
|
Line 33: Line 40:
|-
|-
!5-symbol
!5-symbol
|273
|83
|
|
|
|
|
Line 41: Line 49:
!6-symbol
!6-symbol
|22,302,296
|22,302,296
|
|
|
|
|
Line 47: Line 56:
|}
|}


== Downloadable lists ==
== Downloadable Holdout Lists ==
{| class="wikitable sortable"
{| class="wikitable sortable"
|+
|+
Line 56: Line 65:
!File
!File
!Notes
!Notes
|-
|[[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)]]
|[[BB(6)]]
Line 62: Line 91:
|4,319
|4,319
|[https://docs.google.com/spreadsheets/d/1grhW_0neb2I8TfceN5-v70_3W42Z2U159r9L6FhPGf8/edit?usp=sharing Spreadsheet of holdouts]
|[https://docs.google.com/spreadsheets/d/1grhW_0neb2I8TfceN5-v70_3W42Z2U159r9L6FhPGf8/edit?usp=sharing Spreadsheet of holdouts]
|Keeping track of BB(6) progress.
|Keeping track of BB(6) progress - informal.
|-
|-
|[[BB(3,3)]]
|[[BB(3,3)]]
Line 112: Line 141:
|[[: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 121: Line 157:
|-
|-
|[[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 128: Line 164:
|-
|-
|[[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 135: Line 171:
|-
|-
|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 148: Line 191:
|
|
|-
|-
|[[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 14:55, 18 August 2025

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 unable to decide.

Holdout lists are often shared by contributors. There is a Downloadable Holdout Lists 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.

The table with the "Number of holdouts" is based on the holdout lists listed in the table below it. Thus, some of these numbers have not been independently verified. All the zero entries (no remaining holdouts) have been verified.

Number of holdouts
2-state 3-state 4-state 5-state 6-state 7-state
2-symbol 0 0 0 0 2,728 85,853,789
3-symbol 0 6 460,916,384
4-symbol 0 434,787,751
5-symbol 83
6-symbol 22,302,296

Downloadable Holdout Lists

BB space Date Shared by Number of holdouts File Notes
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=3260"