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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory,sci.logic
Subject: Re: Liar detector: Fred, Richard, Joes and Alan --- Ben's agreement
Date: Mon, 8 Jul 2024 18:04:01 +0200
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Op 08.jul.2024 om 17:04 schreef olcott:
> On 7/8/2024 9:25 AM, Fred. Zwarts wrote:
>> Op 07.jul.2024 om 15:46 schreef olcott:
>>>
>>> Correctly is measured by the semantics of the x86 language.
>>> This specifies that when DDD is correctly simulated by HHH
>>> calls emulated HHH(DDD) that this call cannot return.
>>
>> Yes. This shows that the simulation is incorrect.
>>
>>>
>>> You smash a bottle on the ground. No matter how much you
>>> want the bottle to hold water it will not hold water.
>>
>> Similarly, HHH cannot possibly simulate itself correctly, no matter 
>> how much you want it to be correct, 
> 
> Where correct is understood to be what-ever-the-Hell that the
> machine code of DDD specifies within the semantics of the x86
> language then:
> 
> When DDD is correctly simulated by any pure function x86 emulator
> HHH that aborts its emulation at some point calls HHH(DDD) then
> it is correctly understood that this call cannot possibly return.
> The proof of this is something like mathematical induction.
> 
> When DDD is correctly emulated by any HHH that aborts
> its emulation after N repetitions:
> (1) DDD is correctly emulated by HHH

But only the first part is simulated, not the full input. The simulation 
must simulate the full input. It will will only become correct if also 
the other behaviour of HHH is simulated. But HHH is unable to simulate 
itself up to that point.
That is what the x86 code specifies.

> (2) that calls an emulated HHH(DDD) that
> (3) emulates another DDD... goto (2) or abort

And when it aborts, it is one cycle to soon. One cycle later the 
simulated HHH would abort and return and then DDD would return. That the 
simulating HHH misses that last part, makes the simulation incorrect.

If a simulation misses the return of a program that halts, then the 
simulation is incorrect.
Learn what the x86 code means. The x86 code does not specify an abort. 
When interpreted correctly, it is the description of a program that 
halts. That is the semantics of the x86 code.

> 
> Correct is certainly not screwball misconceptions that contradict
> the above.
> 

As I said, no matter how many time you repeat it, it will not be 
correct, no matter how much you want it to be correct. No matter how 
many different words you use.

The correct simulation of the x86 code shows that the input describes a 
program that aborts and halts.

When HHH aborts itself after N repetitions, N-1 repetitions are 
simulated by the simulation. The simulated HHH is then only one 
repetition away from its own abort and return.
The simulating HHH, misses this behaviour of the program described by 
the input. It does not process the full input, only the first part, up 
to N-1 repetitions. It misses the last repetition, the abort and the 
return. That makes the simulation incorrect.
You may wish that it is correct, but no matter how much you want it, it 
will not become correct. HHH cannot possibly simulate itself correctly. 
It does not matter when it it aborts, it is always one repetition too soon.