Re: Defining a correct halt decider

On 2024-09-02 16:06:11 +0000, olcott said:

A correct halt decider is a Turing machine T with one accept state and one reject state such that:
 If T is executed with initial tape contents equal to an encoding of Turing machine X and its initial tape contents Y, and execution of a real machine X with initial tape contents Y eventually halts, the execution of T eventually ends up in the accept state and then stops.
 If T is executed with initial tape contents equal to an encoding of Turing machine X and its initial tape contents Y, and execution of a real machine X with initial tape contents Y does not eventually halt, the execution of T eventually ends up in the reject state and then stops.

Your "definition" fails to specify "encoding". There is no standard
encoding of Turing machines and tape contents.
--
Mikko