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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory
Subject: Re: Defining a correct halt decider
Date: Wed, 4 Sep 2024 12:17:54 +0200
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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:
>>>
>>> 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.
> 
> 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
> 
> HHH is required to report on the behavior tat its finite
> string input specifies even when this requires HHH
> to emulate itself emulating DDD.
> 
> DDD never halts unless it reaches its own final
> halt state. The fact that the executed HHH halts
> has nothing to do with this.
> 
> 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.

> 
> 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.

> 
> 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.