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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory
Subject: Re: Defining a correct simulating halt decider
Date: Mon, 2 Sep 2024 19:52:48 +0200
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Op 02.sep.2024 om 18:38 schreef olcott:
> A halt decider is a Turing machine that computes
> the mapping from its finite string input to the
> behavior that this finite string specifies.
> 
> If the finite string machine string machine
> description specifies that it cannot possibly
> reach its own final halt state then this machine
> description specifies non-halting behavior.
> 
> A halt decider never ever computes the mapping
> for the computation that itself is contained within.
> 
> Unless there is a pathological relationship between
> the halt decider H and its input D the direct execution
> of this input D will always have identical behavior to
> D correctly simulated by simulating halt decider H.
> 
> *Simulating Termination Analyzer H Not Fooled by Pathological Input D*
> https://www.researchgate.net/ 
> publication/369971402_Simulating_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D
> 
> A correct emulation of DDD by HHH only requires that HHH
> emulate the instructions of DDD** including when DDD calls
> HHH in recursive emulation such that HHH emulates itself
> emulating DDD.

Indeed, it should simulate *itself* and not a hypothetical other HHH 
with different behaviour.
If HHH includes code to see a 'special condition' and aborts and halts, 
then it should also simulate the HHH that includes this same code and 
will halt. It should not assume that the simulated HHH does not have 
this code.

> 
> ** According to the semantics of the x86 language.