Holdouts lists: Difference between revisions
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→Downloadable Holdouts Lists: added a newer BB(4,3) holdouts list |
→Downloadable Holdouts Lists: Added links for dates |
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|March 25th, 2026 | |[https://discord.com/channels/960643023006490684/1239205785913790465/1486207538843222116 March 25th, 2026] | ||
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|February 28th, 2026 | |[https://discord.com/channels/960643023006490684/1239205785913790465/1477224991136419983 February 28th, 2026] | ||
|@mxdys | |@mxdys | ||
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|February 19th, 2026 | |[https://discord.com/channels/960643023006490684/1239205785913790465/1473945366821998684 February 19th, 2026] | ||
|@mxdys | |@mxdys | ||
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|January 29th, 2026 | |[https://discord.com/channels/960643023006490684/1239205785913790465/1466438332677619956 January 29th, 2026] | ||
|@mxdys | |@mxdys | ||
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|[[BB(6)]] | |[[BB(6)]] | ||
|December 30th, 2025 | |[https://discord.com/channels/960643023006490684/1239205785913790465/1455369448264568904 December 30th, 2025] | ||
|@mxdys | |@mxdys | ||
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|December 16th, 2025 | |[https://discord.com/channels/960643023006490684/1239205785913790465/1443989662019354647 December 16th, 2025] | ||
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|November 14th, 2025 | |[https://discord.com/channels/960643023006490684/1239205785913790465/1438983076662477004 November 14th, 2025] | ||
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|October 20th, 2025 | |[https://discord.com/channels/960643023006490684/1239205785913790465/1429892916763033601 October 20th, 2025] | ||
|@mxdys | |@mxdys | ||
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Revision as of 12:00, 31 March 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.
| 2-state | 3-state | 4-state | 5-state | 6-state | 7-state | |
|---|---|---|---|---|---|---|
| 2-symbol | 0 | 0 | 0 | 0 | 1161 | 18,036,852 |
| 3-symbol | 0 | 4 | 9,401,447 | |||
| 4-symbol | 0 | 12,435,284 | ||||
| 5-symbol | 69 | |||||
| 6-symbol | 545,005 |
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.
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(38) | April 19, 2025 | @Sligocki (tab) | Variable (26) | Spreadsheet | |
| 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 |