Holdouts lists: Difference between revisions
→Fractran: added enumeration holdouts list of BBf(22) |
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|[https://discord.com/channels/960643023006490684/1438019511155691521/1448214077028569098 December | |[https://discord.com/channels/960643023006490684/1438019511155691521/1448453530045120657 December 11, 2025] | ||
|@dyuan01 | |||
|10374 | |||
|[https://discord.com/channels/960643023006490684/1438019511155691521/1448453530045120657 message.txt] | |||
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|BBf(22) | |||
|[https://discord.com/channels/960643023006490684/1438019511155691521/1448452369380802720 December 11, 2025] | |||
|@dyuan01 | |||
|10593 | |||
|[https://discord.com/channels/960643023006490684/1438019511155691521/1448452369380802720 message.txt] | |||
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|BBf(22) | |||
|[https://discord.com/channels/960643023006490684/1438019511155691521/1448451881998352484 December 11, 2025] | |||
|@dyuan01 | |||
|11000 | |||
|[https://discord.com/channels/960643023006490684/1438019511155691521/1448451881998352484 message.txt] | |||
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|- | |||
|BBf(22) | |||
|[https://discord.com/channels/960643023006490684/1438019511155691521/1448449345371504722 December 11, 2025] | |||
|@dyuan01 | |||
|52915 | |||
|[https://discord.com/channels/960643023006490684/1438019511155691521/1448449345371504722 message.txt] | |||
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|- | |||
|BBf(22) | |||
|[https://discord.com/channels/960643023006490684/1438019511155691521/1448214077028569098 December 10, 2025] | |||
|@-d | |@-d | ||
|91123 | |91123 | ||
Revision as of 18:47, 28 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 | 548,993 |
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 |
Fractran
| Domain | Date | Shared by | Number of holdouts | File | Notes |
|---|---|---|---|---|---|
| BBf(22) | December 11, 2025 | @dyuan01 | 10374 | message.txt | |
| BBf(22) | December 11, 2025 | @dyuan01 | 10593 | message.txt | |
| BBf(22) | December 11, 2025 | @dyuan01 | 11000 | message.txt | |
| BBf(22) | December 11, 2025 | @dyuan01 | 52915 | 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) has since been solved |
| 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(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 |