1RB0LE 1LC1RA ---1LD 0RB1LF 1RD1LA 0LA0RD: Difference between revisions
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the next two (1RB0LE_1LC1RA_---1LD_0RB1LF_1RD1LA_1RD0LA and 1RB0LE_1LC1RA_---1LD_0RB1LF_1RD1LA_0LA0LA) are clearly equivalent to it, so also non-halting | the next two (1RB0LE_1LC1RA_---1LD_0RB1LF_1RD1LA_1RD0LA and 1RB0LE_1LC1RA_---1LD_0RB1LF_1RD1LA_0LA0LA) are clearly equivalent to it, so also non-halting | ||
</pre> | </pre> | ||
==== Incorrect probviously halting argument ==== | |||
Assuming that the remainders mod 6 are independent and uniformly distributed from 0 to 5 predicts that the machine must halt with probability 1. But, the machine is nonhalting. | |||
Revision as of 13:49, 8 August 2025
1RB0LE_1LC1RA_---1LD_0RB1LF_1RD1LA_0LA0RD (bbch) is a non-halting BB(6) Turing machine.
Analysis by @racheline on 29 July 2024 (Discord link):
1RB0LE_1LC1RA_---1LD_0RB1LF_1RD1LA_0LA0RD A(n) = 0^inf <A 0 1^n rules: A(6n) -> A(12n+3) A(6n+1) -> A(12n+6) A(6n+2) -> halt A(6n+3) -> A(9n+9) A(6n+4) -> halt A(6n+5) -> A(9n+12) start from A(3) as we can see, everything that doesn't halt goes to A(6m) or A(6m+3) for some m, so halting is unreachable the next two (1RB0LE_1LC1RA_---1LD_0RB1LF_1RD1LA_1RD0LA and 1RB0LE_1LC1RA_---1LD_0RB1LF_1RD1LA_0LA0LA) are clearly equivalent to it, so also non-halting
Incorrect probviously halting argument
Assuming that the remainders mod 6 are independent and uniformly distributed from 0 to 5 predicts that the machine must halt with probability 1. But, the machine is nonhalting.