1RB1RC 1LC1LE 1RA1RD 0RF0RE 1LA0LB ---1RA: Difference between revisions
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{{machine|1RB1RC_1LC1LE_1RA1RD_0RF0RE_1LA0LB_---1RA}} | {{machine|1RB1RC_1LC1LE_1RA1RD_0RF0RE_1LA0LB_---1RA}}{{unsolved|Does this TM run forever?}} | ||
This is a [[BB(6)]] [[Cryptid]] found by @mxdys and shared on Discord on 27 Jul 2024. It's closely related to [[Hydra]] and [[Antihydra]]. | This is a [[BB(6)]] [[Cryptid]] found by @mxdys and shared on Discord on 27 Jul 2024. It's closely related to [[Hydra]] and [[Antihydra]]. | ||
Revision as of 01:35, 9 July 2025
Unsolved problem:
Does this TM run forever?
This is a BB(6) Cryptid found by @mxdys and shared on Discord on 27 Jul 2024. It's closely related to Hydra and Antihydra.
Analysis by @mxdys
antihydra variant: 1RB1RC_1LC1LE_1RA1RD_0RF0RE_1LA0LB_---1RA (n,m) := 0^inf C> 01011 01^n 1 01^m 0^inf start from (3,1) (2n+1,m) --> (3n+3,m+2) (2n,m+1) --> (3n+3,m) (4n,0) --> (9n+6,1) (4n+2,0) --> halt
The rules are proved in Coq.
Analysis by @dyuan01
Using B(a, b) = (3a-6, b), I've come up with these rules:
Start from B(3, 1) B(2n, m+1) → B(3n, m) B(2n+1, m) → B(3n+1, m+2) B(4n+2, 0) → B(9n+4, 1) B(4n, 0) → halt
This is actually just Hydra except you start at B(3, 1) instead of B(3, 0) and you don't necessarily halt if you reach -1. In fact, this can only halt if Hydra halts.