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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory,sci.logic,comp.ai.philosophy
Subject: Re: The error of the standard proof of the halting problem
Date: Wed, 23 Jul 2025 10:20:17 +0200
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Op 22.jul.2025 om 18:09 schreef olcott:
> On 7/22/2025 3:45 AM, Fred. Zwarts wrote:
>> Op 22.jul.2025 om 06:17 schreef olcott:
>>> On 7/21/2025 9:20 PM, Richard Damon wrote:
>>>> On 7/21/25 9:45 AM, olcott wrote:
>>>>> On 7/21/2025 4:06 AM, Mikko wrote:
>>>>>> On 2025-07-20 11:48:37 +0000, Mr Flibble said:
>>>>>>
>>>>>>> On Sun, 20 Jul 2025 07:13:43 -0400, Richard Damon wrote:
>>>>>>>
>>>>>>>> On 7/20/25 12:58 AM, olcott wrote:
>>>>>>>>> Title: A Structural Analysis of the Standard Halting Problem Proof
>>>>>>>>>
>>>>>>>>> Author: PL Olcott
>>>>>>>>>
>>>>>>>>> Abstract:
>>>>>>>>> This paper presents a formal critique of the standard proof of the
>>>>>>>>> undecidability of the Halting Problem. While we do not dispute the
>>>>>>>>> conclusion that the Halting Problem is undecidable, we argue 
>>>>>>>>> that the
>>>>>>>>> conventional proof fails to establish this conclusion due to a
>>>>>>>>> fundamental misapplication of Turing machine semantics. 
>>>>>>>>> Specifically,
>>>>>>>>> we show that the contradiction used in the proof arises from 
>>>>>>>>> conflating
>>>>>>>>> the behavior of encoded simulations with direct execution, and 
>>>>>>>>> from
>>>>>>>>> making assumptions about a decider's domain that do not hold 
>>>>>>>>> under a
>>>>>>>>> rigorous model of computation.
>>>>>>>>>
>>>>>>>> Your problem is you don't understand the meaning of the words 
>>>>>>>> you are
>>>>>>>> using.
>>>>>>>
>>>>>>> This is an ad hominem attack, not argumentation.
>>>>>>
>>>>>> It is also honest and truthful, which is not as common as it should.
>>>>>>
>>>>>
>>>>> It is also honest and truthful that people
>>>>> that deny verified facts are either liars
>>>>> or lack sufficient technical competence.
>>>>>
>>>>
>>>> Right, so YOU are the liar.
>>>>
>>>> It is a verified fact that the PROGRAM DDD halts since your HHH(DDD) 
>>>> returns 0.
>>>>
>>>
>>> It is a self-evident truth that the halting problem proof
>>> has always been incorrect when it requires a halt decider
>>> to report on the behavior of the direct execution of any
>>> Turing machine because no Turing machine decider can ever
>>> take another directly executed Turing machine as its input.
>> As usual incorrect claims without evidence.
>> Nobody requires the halt decider to report on another direct execution.
> 
> counter-factual

As usual incorrect claims without evidence.

> 
> The *domain of this problem is to be taken as the*
> *set of all Turing machines* [WRONG] and all w;
> 
> that is, we are
> looking for a single Turing machine that, given the
> description of an arbitrary M and w, will predict
> whether or not the computation of M applied to w will halt.
> https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf

Note the 'given the description of an arbitrary M". It does not say 
'given an arbitrary M'. The word 'description' makes your claim 
counter-factual.

> 
>> The halt decider must decide on its input. In this case the input 
>> specifies a DD that calls a HHH that aborts and returns, so the input 
>> specifies a halting program.
> 
> The simulated DDD that calls a simulated HHH(DDD)
> never aborts or returns.

But the HHH called by DDD is programmed to abort after a finite 
recursion. The behaviour of DDD depends on the behaviour of HHH. When 
HHH returns with a value of 0, DDD reaches the final halt state.
That is what is specified. That is what a correct simulation would see.

> 
> The directly executed HHH aborts its simulation
> of DDD which in turn kills the whole simulation
> process that includes the simulated HHH.
HHH aborts before it reaches the final halt state. There is nothing in 
the simulation that shows that there is no final halt state. In fact, 
HHH ignores the conditional branch instructions during the simulation, 
which could tell it that there is a final halt state.

Nowhere there is a reference to direct execution. It is only the 
semantics of the x86 language that tells enough to prove the halting 
behaviour of the program specified in the input. That HHH fails to 
simulate he input up to the end, does not change the specification.