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
|
| 2-symbol
|
0
|
0
|
0
|
0
|
2,891
|
| 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
|
File:BB6 holdouts 2728.txt
|
| BB(2,5)
|
March 29 2025
|
@mxdys
|
83
|
|
| 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
|
|