Re: Title: A Structural Analysis of the Standard Halting Problem Proof

Op 21.jul.2025 om 15:57 schreef olcott:

On 7/21/2025 4:10 AM, Mikko wrote:

On 2025-07-20 15:36:51 +0000, olcott said:
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On 7/20/2025 8:05 AM, Alan Mackenzie wrote:

[ Followup-To: set ]
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In comp.theory Mr Flibble <flibble@red-dwarf.jmc.corp> wrote:

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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Maybe it was you wanting to create that impression by dishonestly
snipping the substance of Richard's post, where he illustrated some of
the words whose meaning PO fails to understand.

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It never has been that I do not understand
the definitions of words it is that I have
proven that some of these definitions are incorrect.

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That you think a definition is incorrect does not change the defined
meaning. If you don't accept the definition the best you can do is
that you don't use the term.
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 That I prove that a definition is derived from provably
false assumptions proves that this definition is incorrect.

As usual incorrect claims without evidence. Nobody ever saw the proof.>

No one here is capable of paying enough attention to my
proof that the halting problem definition is incorrect
because my proof requires two steps and no one here can
even pay attention to one step.

Even the first step has many errors. But you close your eyes and pretend that nobody showed these errors to you.

 *This right here is a type mismatch error*
The simplest step is that no Turing machine decider
ever takes another directly executing Turing machine
as its input yet the halting problem requires a halt
decider to report on the behavior of the directly
executed machine.

Nobody require the decider to report on the direct execution of another machine. But if the input specifies a halting program, but HHH is unable to report that, HHH just fails.

 This would not be an issue if the correct simulation
of a Turing machine description always had the exact
same behavior as the directly executed machine.

It has, because that is the definition of behaviour. The semantics of the x86 language does not allow multiple interpretations for the behaviour. The same holds for other machine languages.

 Everyone here sees that the behavior is not the same
and rules that the simulation is wrong because it
differs from the behavior of the direct execution.
*That is an incorrect measure of correct simulation*
 

We only see that HHH fails to do a correct simulation up to the end, because of a premature abort. We see bugs in HHH, where it concludes from a finite recursion that there is a non-halting behaviour.