Holdouts lists: Difference between revisions
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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 [[Decider|deciders]] are yet unable to decide. | 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 [[Decider|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 [[Tree Normal Form|TNF enumeration]]. | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 20: | Line 16: | ||
|0 | |0 | ||
|0 | |0 | ||
| | |1314 | ||
| | |19,303,801 | ||
|- | |- | ||
!3-symbol | !3-symbol | ||
|0 | |0 | ||
| | |4 | ||
|9,401,447 | |9,401,447 | ||
| | | | ||
| Line 33: | Line 29: | ||
!4-symbol | !4-symbol | ||
|0 | |0 | ||
| | |12,435,284 | ||
| | | | ||
| | | | ||
| Line 48: | Line 44: | ||
|- | |- | ||
!6-symbol | !6-symbol | ||
| | |558,039 | ||
| | | | ||
| | | | ||
| Line 57: | Line 53: | ||
== Downloadable Holdout Lists == | == Downloadable Holdout 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. | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ | |+ | ||
| Line 67: | Line 64: | ||
|- | |- | ||
|[[BB(6)]] | |[[BB(6)]] | ||
| | |January 29th, 2026 | ||
|@mxdys | |||
|1314 | |||
|[https://discord.com/channels/960643023006490684/1239205785913790465/1466438332677619956 BB6_holdouts_1314.txt] | |||
| | |||
|- | |||
|[[BB(6)]] | |||
|December 30th, 2025 | |||
|@mxdys | |@mxdys | ||
| | |1326 | ||
|[https://wiki.bbchallenge.org/w/images/ | |[https://wiki.bbchallenge.org/w/images/f/f0/BB6_holdouts_1326.txt BB6_holdouts_1326.txt] | ||
| | | | ||
|- | |- | ||
| Line 76: | Line 80: | ||
|November 22nd, 2025 | |November 22nd, 2025 | ||
|Robin Rovenszky | |Robin Rovenszky | ||
| | |Variable (1325) | ||
|[https://docs.google.com/spreadsheets/d/ | |[https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Google Sheets] | ||
|Annotated list, including links to Discord discussions | |Annotated list, including links to Discord discussions, always up-to-date. | ||
|- | |||
|[[BB(6)]] | |||
|December 16th, 2025 | |||
|@mxdys | |||
|1343 | |||
|[https://wiki.bbchallenge.org/w/images/9/9a/BB6_holdouts_classified_1343.txt BB6_holdouts_1343.txt] | |||
| | |||
|- | |||
|[[BB(6)]] | |||
|November 28th, 2025 | |||
|@mxdys | |||
|1416 | |||
|[https://wiki.bbchallenge.org/w/images/9/98/BB6_holdouts_1416.txt BB6_holdouts_1416.txt] | |||
| | |||
|- | |- | ||
|[[BB(6)]] | |[[BB(6)]] | ||
Latest revision as of 15:49, 2 February 2026
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 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 | 1314 | 19,303,801 |
| 3-symbol | 0 | 4 | 9,401,447 | |||
| 4-symbol | 0 | 12,435,284 | ||||
| 5-symbol | 75 | |||||
| 6-symbol | 558,039 |
Downloadable Holdout 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.