Re: Defining a correct halt decider

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:
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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.

 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,

except in olcott's crippled example, where he places the code of the simulating HHH inside the finite string of its input.
The finite string containing the description of DDD and all functions called by it including HHH) should not be placed in the same memory location as the simulator's code and variables.
 

>
That no one has noticed that they can differ does not
create an axiom where they are not allowed to differ.

 By twisting the code and the examples in such ways that the simulation is crippled, you do not prove that they show anything useful.
 

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No one noticed that they differ only because everyone
rejected the idea of a simulating halt decider out-of-hand
without review.
>

Olcott is a strange person. At the one hand he is begging for reviews, but he is so arrogant that he does not want to learn anything from the reviews. He has such a strong belief in his ideas, that he thinks that reviewers are lying if the prove that he is incorrect.