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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Overview of proof that the input to HHH(DDD) specifies non-halting behavior --- Mike
Date: Wed, 14 Aug 2024 11:09:46 +0300
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On 2024-08-13 13:04:17 +0000, olcott said:

> On 8/13/2024 5:57 AM, Mikko wrote:
>> On 2024-08-13 01:43:49 +0000, olcott said:
>> 
>>> We prove that the simulation is correct.
>>> Then we prove that this simulation cannot possibly
>>> reach its final halt state / ever stop running without being aborted.
>>> The semantics of the x86 language conclusive proves this is true.
>>> 
>>> Thus when we measure the behavior specified by this finite
>>> string by DDD correctly simulated/emulated by HHH it specifies
>>> non-halting behavior.
>>> 
>>> https://www.researchgate.net/ 
>>> publication/369971402_Simulating_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D 
>>> 
>> 
>> Input to HHH(DDD) is DDD. If there is any other input then the proof is
>> not interesting.
>> 
>> The behviour specified by DDD on the first page of the linked article
>> is halting if HHH(DDD) halts. Otherwise HHH is not interesting.
>> 
>> Any proof of the false statement that "the input to HHH(DDD) specifies
>> non-halting behaviour" is either uninteresting or unsound.
>> 
> 
> void DDD()
> {
>    HHH(DDD);
>    return;
> }
> 
> It is true that DDD correctly emulated by any HHH cannot
> possibly reach its own "return" instruction final halt state.

If DDD does not halt then HHH does not halt.

-- 
Mikko