Re: Defining a correct halt decider

On 2024-09-03 13:17:56 +0000, olcott said:

On 9/3/2024 3:44 AM, Mikko wrote:

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.

 That is why I made the isomorphic x86utm system.
By failing to have such a concrete system all kinds
of false assumptions cannot be refuted.

If it were isnomorphic the same false assumtipns would apply to both.

The behavior of DDD emulated by HHH** <is> different
than the behavior of the directly executed DDD**
**according to the semantics of the x86 language

The halting problem is not about a string but about a behaviour.
Your decider is not a halt decider if it answers about another
behaviour.
--
Mikko