Holdouts lists: Difference between revisions
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→Busy Beaver for Lambda Calculus: updated holdout counts |
Updated BB(4,3), BBlambda(41) and BBlambda(42) holdout counts |
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|[https://discord.com/channels/960643023006490684/1355653587824283678/1517130491512492083 June 18, 2026] | |[https://discord.com/channels/960643023006490684/1355653587824283678/1517130491512492083 June 18, 2026] | ||
|@C++DSucker | |@C++DSucker | ||
|Variable ( | |Variable (240) | ||
|[https://docs.google.com/spreadsheets/d/1jZ6TK9m3xmXUlC69727T-8WwvhALcsp8FrK6DzgThtw/edit?gid=1544675322#gid=1544675322 Spreadsheet] | |[https://docs.google.com/spreadsheets/d/1jZ6TK9m3xmXUlC69727T-8WwvhALcsp8FrK6DzgThtw/edit?gid=1544675322#gid=1544675322 Spreadsheet] | ||
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|Variable ( | |Variable (8) | ||
|[https://docs.google.com/spreadsheets/d/1jZ6TK9m3xmXUlC69727T-8WwvhALcsp8FrK6DzgThtw/edit?gid=1502335946#gid=1502335946 Spreadsheet] | |[https://docs.google.com/spreadsheets/d/1jZ6TK9m3xmXUlC69727T-8WwvhALcsp8FrK6DzgThtw/edit?gid=1502335946#gid=1502335946 Spreadsheet] | ||
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Revision as of 09:41, 25 July 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 | 1094 | 15,743,264 |
| 3-symbol | 0 | 4 | 4,747,566 | |||
| 4-symbol | 0 | 11,362,197 | ||||
| 5-symbol | 65 | |||||
| 6-symbol | 412,086 |
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(23) | July 11, 2026 | @-d | 21233 | sz23_21233.txt | |
| BBf(23) | June 3, 2026 | @-d | 21295 | sz23_21295.txt | Programs simulated to halting were removed |
| BBf(23) | June 2, 2026 | @-d | 21320 | sz23_21320.txt | Programs simluated to halting were removed |
| BBf(23) | June 2, 2026 | @-d | 28100 | sz23_28100.txt | |
| BBf(23) | June 2, 2026 | @-d | 29188 | sz23_29188.txt | |
| BBf(23) | May 31, 2026 | @-d | 29250 | sz23_29250.txt | |
| BBf(23) | May 31, 2026 | @-d | 94367 | sz23_94367.txt | |
| BBf(23) | May 30, 2026 | @-d | 790,335 | sz23_790335.txt | |
| BBf(22) | April 4, 2026 | @-d | 3 | sz22_3.txt | Holdout reduction by Claude Opus 4.6 |
| 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(42) | June 18, 2026 | @C++DSucker | Variable (240) | Spreadsheet | |
| BBλ(41) | Variable (8) | Spreadsheet | |||
| BBλ(40) | June 10, 2026 | @C++DSucker | 0 | Spreadsheet | BBλ(40) was solved on July 20th, 2026 |
| BBλ(39) | April 10, 2026 | @Sligocki | 0 | Spreadsheet | BBλ(39) was solved on June 10th, 2026 |
| BBλ(38) | April 19, 2025 | @Sligocki | 0 | Spreadsheet | BBλ(38) was solved on April 13th, 2026 |
| 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 |
CounterScript
| Domain | Date | Shared by | Number of holdouts | File | Notes |
|---|---|---|---|---|---|
| BBCS(11) | July 10, 2026 | @Azerty | 1 | 11.txt |