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. Here is a table that summarises the number of holdout per busy beaver domain:
Number of holdouts
|
|
2-state
|
3-state
|
4-state
|
5-state
|
6-state
|
| 2-symbol
|
0
|
0
|
0
|
0
|
4408
|
| 3-symbol
|
0
|
6
|
460,916,384
|
|
|
| 4-symbol
|
0
|
434,787,751
|
|
|
|
| 5-symbol
|
273
|
|
|
|
|
| 6-symbol
|
22,302,296
|
|
|
|
|
Downloadable lists
| BB space
|
Date
|
Shared by
|
Number of holdouts
|
File
|
Notes
|
| 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 15th 2024
|
@dyuan01
|
273
|
File:2x5_holdouts_273.txt
|
@Justin Blanchard's 499 holdouts minus machines solved by @mxdys
|
| BB(6)
|
June 13th 2024
|
@tjligocki
|
12,091
|
File:BB6 holdouts 12091.txt
|
Work done with @Shawn Ligocki
|
| BB(3,3)
|
June 9th 2024
|
@Justin Blanchard
|
22
|
File:3x3.todo.txt, File:Mugshots small.pdf
|
|
| BB(6)
|
June 7th 2024
|
@mxdys
|
12,325
|
File:BB6 holdouts 12325.txt
|
Some equivalent machines are removed.
|
| BB(2,5)
|
May 22nd 2024
|
@Justin Blanchard
|
499
|
File:2x5.todo.txt
|
|
| BB(5)
|
|
|
0
|
|
|
Georgi Georgiev (Skelet) posted 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.