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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 12:06:40 -0500
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On 5/11/2025 11:59 AM, Mr Flibble wrote:
> On Sun, 11 May 2025 11:49:51 -0500, olcott wrote:
> 
>> 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.
> 
> Nevertheless it is impossible to obtain a halting result as the problem is
> ill-formed: mapping a halting result of non-halting to the infinite
> recursion manifesting due to type mismatch is entirely artificial.
> 
> /Flibble 

When a simulating termination analyzer examines
the behavior that its input actually specifies
and reports on this, then in the case of every
conventional Halting Problem proof it is correct
to reject this input as non-halting.


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