Cryptids: Difference between revisions
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'''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 | '''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, most currently known Cryptids have [[Collatz-like]] behavior. In other words, the halting problem from blank tape of cryptids is mathematically-hard. | ||
If there exists a Cryptid with n states and m symbols, then BB(n, m) cannot be solved without solving this hard math problem. | If there exists a Cryptid with n states and m symbols, then BB(n, m) cannot be solved without solving this hard math problem. | ||
Revision as of 13:14, 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, most currently known Cryptids have Collatz-like behavior. In other words, the halting problem from blank tape of cryptids is mathematically-hard.
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 |
|---|---|---|---|---|---|---|
| Goldbach | BB(27) | https://gist.github.com/anonymous/a64213f391339236c2fe31f8749a0df6(unverified) | 2016 | anonymous | The machine halts if and only if Golbach's conjecture is false. To the best of our knowledge this construction has not been independently verified. | |
| Erdős | BB(5,4) and
BB(15) |
arxiv preprint | Jul 2021 | Tristan Stérin (@cosmo) 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" | |
| Weak Collatz | BB(124) and BB(43,4) | https://docs.bbchallenge.org/other/weak_Collatz_conjecture_124_2.txt (unverified)
https://docs.bbchallenge.org/other/weak_Collatz_conjecture_43_4.txt (unverified) |
Jul 2021 | Tristan Stérin | The machine halts if and only if the "weak Collatz conjecture" is false. The weak Collatz conjecture states that the iterated Collatz map (3x+1) has only one cycle on the positive integers.
Not independently verified, and probably easy to further optimise. | |
| 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.