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

On 7/22/2025 6:39 AM, Richard Damon wrote:

On 7/22/25 12:17 AM, olcott wrote:

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.

 If it seems "self-evident" to you, that just shows how warped you ideas are of what the field means.
 

In this field it is common knowledge that no Turing machine
decider ever takes another directly executed Turing machine
as its input.
This means that Linz is wrong that machine M
should report on the behavior of its own direct
execution as his words state below.
WM is the machine description of M
q0 WM ⊢* Ĥq0 WM WM ⊢* Ĥ∞,
    if M applied to WM halts, and
q0 WM ⊢* Ĥq0 Wm WM ⊢* Ĥ y1 qn y2,
    if M applied to WM does not halt.
TM's can only compute the mapping from inputs and M
is not an input.
https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer