Re: The error of the standard proof of the halting problem

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:
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On Sun, 20 Jul 2025 07:13:43 -0400, Richard Damon wrote:
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On 7/20/25 12:58 AM, olcott wrote:

Title: A Structural Analysis of the Standard Halting Problem Proof
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Author: PL Olcott
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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.
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Your problem is you don't understand the meaning of the words you are
using.

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This is an ad hominem attack, not argumentation.

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It is also honest and truthful, which is not as common as it should.
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It is also honest and truthful that people
that deny verified facts are either liars
or lack sufficient technical competence.
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Right, so YOU are the liar.
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It is a verified fact that the PROGRAM DDD halts since your HHH(DDD) returns 0.
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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
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

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.
The directly executed HHH aborts its simulation
of DDD which in turn kills the whole simulation
process that includes the simulated HHH.

That HHH fails to see that does not change the specification.
That this input specifies a halting program, is proven in many ways, of which the direct execution is only one of them.

--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer