Re: Defining a correct halt decider

Op 04.sep.2024 om 15:59 schreef olcott:

On 9/4/2024 5:17 AM, Fred. Zwarts wrote:

Op 03.sep.2024 om 15:17 schreef olcott:

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:
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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.
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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.

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

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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.
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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
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HHH is required to report on the behavior tat its finite
string input specifies even when this requires HHH
to emulate itself emulating DDD.
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DDD never halts unless it reaches its own final
halt state. The fact that the executed HHH halts
has nothing to do with this.
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HHH is not allowed to report on the computation that
itself is contained within.

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But it must be able to process a finite string containing a copy of itself, or containing a similar algorithm.
>

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Except for the case of pathological self-reference the
behavior of the directly executed machine M is always
the same as the correctly simulated finite string ⟨M⟩.

>
There is no self-reference,

 It is very stupid to say that when this proves there is
https://github.com/plolcott/x86utm/blob/master/Halt7out.txt
 

Olcott does not understand that HHH must process its input, a finite string describing a program. That finite string is not a self-reference. It may include a copy of the simulator, or the same algorithm expressed in a different way.
But olcott is confused, because he incorrectly makes it a self-reference, by placing the simulating HHH and the finite string in such a way in memory, that they overlap. He even uses the address of HHH in the finite string. With such errors, it is not surprising that he thinks it is a self-reference, but that is only because of his incorrect coding of the problem.