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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: =?UTF-8?Q?Re=3A_Flibble=E2=80=99s_Leap=3A_Why_Behavioral_Divergence?=
 =?UTF-8?Q?_Implies_a_Type_Distinction_in_the_Halting_Problem?=
Date: Sun, 11 May 2025 11:49:51 -0500
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On 5/11/2025 11:05 AM, Mr Flibble wrote:
> On Sun, 11 May 2025 10:56:02 -0500, olcott wrote:
> 
>> On 5/11/2025 10:49 AM, Mr Flibble wrote:
>>> On Sun, 11 May 2025 16:47:09 +0100, Richard Heathfield wrote:
>>>
>>>> On 11/05/2025 16:34, Mr Flibble wrote:
>>>>> On Sun, 11 May 2025 16:25:14 +0100, Richard Heathfield wrote:
>>>>>
>>>>>> For a question to be semantically incorrect, it takes more than just
>>>>>> you and your allies to be unhappy with it.
>>>>>
>>>>> For a question to be semantically correct, it takes more than just
>>>>> you and your allies to be happy with it.
>>>>
>>>> Indeed. It has to have meaning. It does. That meaning has to be
>>>> understood by sufficiently intelligent people. It is.
>>>>
>>>> You don't like the question. I get that. I don't know /why/ you don't
>>>> like it, because all your explanations to date have been complete
>>>> expletive deleted. For a Usenet article to be semantically correct, it
>>>> helps if your readers can understand what the <exp. del.> you're
>>>> talking about.
>>>>
>>>> What I get from your stand is that you agree with olcott that a
>>>> 'pathological' input halts... no, never halts... well, you can't
>>>> decide between you, but you're agreed that it's definitely decidable,
>>>> right?
>>>
>>> Re-read the OP for my answer:
>>>
>>> Flibble’s Leap: Why Behavioral Divergence Implies a Type Distinction in
>>> the Halting Problem
>>>
> ===========================================================================================
>>>
>>> Summary -------
>>> Flibble argues that the Halting Problem's undecidability proof is built
>>> on a category (type) error: it assumes a program and its own
>>> representation (as a finite string) are interchangeable. This
>>> assumption fails under simulating deciders, revealing a type
>>> distinction through behavioral divergence. As such, all deciders must
>>> respect this boundary, and diagonalization becomes ill-formed. This
>>> reframing dissolves the paradox by making the Halting Problem itself an
>>> ill-posed question.
>>>
>>> 1. Operational Evidence of Type Distinction
>>> -------------------------------------------
>>> - When a program (e.g., `DD()`) is passed to a simulating halt decider
>>> (`HHH`), it leads to infinite recursion.
>>> - This behavior differs from direct execution (e.g., a crash due to a
>>> stack overflow).
>>
>> The directly executed DD() simply halts because HHH has stopped the
>> infinite recursion that it specifies on its second recursive call.
> 
> That behaviour is due to a decision you have made, that I disagree with,
> the correct thing to do is to allow infinite recursion to manifest as
> stack overflow rather than return an artificial halting result.
> 

That fails to meet the spec of a termination analyzer.

>>
>> DD emulated by HHH according to the rules of the x86 language cannot
>> possibly halt. Because all deciders are required to report on what their
>> finite string input specifies HHH must reject DD as non-halting.
> 
> The category error precludes a decision being made as the problem is ill-
> formed.
> 
> /Flibble

int sum(int x, int y) { return x + y; }

The category error is actually the fact that everyone
here expects a termination analyzer to report on behavior
other than the behavior that its input finite string
actually specifies.

This is only uncomputable in the same way that sum(3,2)
cannot compute the sum of 5 + 7.

We could call this the can't compute the wrong sum problem.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer