Cryptids: Difference between revisions
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! Name !! BB domain !! Machine !! Announcement !! Discoverer !! Note | ! Name !! BB domain !! Machine !! Announcement !! Date !! Discoverer !! Note | ||
|- Erdős || BB(15) || || [https://arxiv.org/abs/2107.12475 arxiv preprint] || Jul 2021 || Tristan Stérin (<code>@cosmo</code>) and Damien Woods || The machine halts if and only if the following conjecture by Erdős is false: "For all n > 8, there is at least one 2 in the base-3 representation of 2^n" | |||
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| Bigfoot || [[BB(3, 3)]]|| <code>1RB2RA1LC_2LC1RB2RB_---2LA1LA</code>|| [https://www.sligocki.com/2023/10/16/bb-3-3-is-hard.html BB(3, 3) is hard] || [[User:Sligocki|Shawn Ligocki]] || | | Bigfoot || [[BB(3, 3)]]|| <code>1RB2RA1LC_2LC1RB2RB_---2LA1LA</code>|| [https://www.sligocki.com/2023/10/16/bb-3-3-is-hard.html BB(3, 3) is hard] || Nov 2023 || [[User:Sligocki|Shawn Ligocki]] || | ||
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| Hydra || [[BB(2, 5)]]|| <code>1RB3RB---3LA1RA_2LA3RA4LB0LB0LA</code>|| [https://www.sligocki.com/2024/05/10/bb-2-5-is-hard.html BB(2, 5) is hard] || Daniel Yuan || | | Hydra || [[BB(2, 5)]]|| <code>1RB3RB---3LA1RA_2LA3RA4LB0LB0LA</code>|| [https://www.sligocki.com/2024/05/10/bb-2-5-is-hard.html BB(2, 5) is hard] || May 2024 || Daniel Yuan || | ||
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| || BB(2, 5) || <code>1RB3RB---3LA1RA_2LA3RA4LB0LB1LB</code>||[https://www.sligocki.com/2024/05/10/bb-2-5-is-hard.html#a-bonus-cryptid A Bonus Cryptid] || Daniel Yuan || | | || BB(2, 5) || <code>1RB3RB---3LA1RA_2LA3RA4LB0LB1LB</code>||[https://www.sligocki.com/2024/05/10/bb-2-5-is-hard.html#a-bonus-cryptid A Bonus Cryptid] || May 2024 || Daniel Yuan || | ||
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| || [[BB(7, 2)]]|| <code>0RB1RB_1LC0RA_1RE1LF_1LF1RE_0RD1RD_1LG0LG_---1LB</code>|| [https://github.com/sligocki/sligocki.github.io/issues/8#issuecomment-2140887228 Bigfoot Comment] || <code>@Iijil1</code>|| Compilation of Bigfoot into 2 symbols | | || [[BB(7, 2)]]|| <code>0RB1RB_1LC0RA_1RE1LF_1LF1RE_0RD1RD_1LG0LG_---1LB</code>|| [https://github.com/sligocki/sligocki.github.io/issues/8#issuecomment-2140887228 Bigfoot Comment] || June 2024 || <code>@Iijil1</code>|| Compilation of Bigfoot into 2 symbols, there was a previous compilation [https://github.com/sligocki/sligocki.github.io/issues/8#issuecomment-1774200442 with 8 states] | ||
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| || BB(10, 2) || <code>0RE1RG_1RH0LD_0LA0LF_0LB1LJ_1RB1RA_1RE1LC_0LF---_1LF0LI_0LD0LC_1RE0RH</code>|| || Daniel Yuan || Compilation of Hydra into 2 symbols | | || BB(10, 2) || <code>0RE1RG_1RH0LD_0LA0LF_0LB1LJ_1RB1RA_1RE1LC_0LF---_1LF0LI_0LD0LC_1RE0RH</code>|| [https://discord.com/channels/960643023006490684/1084047886494470185/1247560072427474955 Discord message] || June 2024 || Daniel Yuan || Compilation of Hydra into 2 symbols | ||
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Revision as of 12:57, 9 June 2024
Cryptids are Turing Machines whose behavior (when started on a blank tape) can be described completely by a relatively simple mathematical rule, but where that rule falls into a class of unsolved (and presumed hard) mathematical problems. This definition is somewhat subjective (What counts as a simple rule? What counts as a hard problem?). In practice all current known Cryptids have Collatz-like behavior.
If there exists a Cryptid with n states and m symbols, then BB(n, m) cannot be solved without solving this hard math problem.
The name Cryptid was proposed by Shawn Ligocki in an Oct 2023 blog post announcing the first discovered Cryptid: Bigfoot.
List of Cryptids
| Name | BB domain | Machine | Announcement | Date | Discoverer | Note |
|---|---|---|---|---|---|---|
| Bigfoot | BB(3, 3) | 1RB2RA1LC_2LC1RB2RB_---2LA1LA |
BB(3, 3) is hard | Nov 2023 | Shawn Ligocki | |
| Hydra | BB(2, 5) | 1RB3RB---3LA1RA_2LA3RA4LB0LB0LA |
BB(2, 5) is hard | May 2024 | Daniel Yuan | |
| BB(2, 5) | 1RB3RB---3LA1RA_2LA3RA4LB0LB1LB |
A Bonus Cryptid | May 2024 | Daniel Yuan | ||
| BB(7, 2) | 0RB1RB_1LC0RA_1RE1LF_1LF1RE_0RD1RD_1LG0LG_---1LB |
Bigfoot Comment | June 2024 | @Iijil1 |
Compilation of Bigfoot into 2 symbols, there was a previous compilation with 8 states | |
| BB(10, 2) | 0RE1RG_1RH0LD_0LA0LF_0LB1LJ_1RB1RA_1RE1LC_0LF---_1LF0LI_0LD0LC_1RE0RH |
Discord message | June 2024 | Daniel Yuan | Compilation of Hydra into 2 symbols |
Beeping Busy Beaver
Cryptids were actually noticed in the Beeping Busy Beaver problem before they were in the classic Busy Beaver. See Mother of Giants describing a "family" of Turing machines which "probviously" quasihalt, but requires solving a Collatz-like problem in order to actually prove it. They are all TMs formed by filling in the missing transition in 1RB1LE_0LC0LB_0LD1LC_1RD1RA_---0LA with different values.