Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Keith Thompson <Keith.S.Thompson+u@gmail.com>
Newsgroups: comp.theory
Subject: Re: =?utf-8?Q?Flibble=E2=80=99s?= Leap: Why Behavioral Divergence
 Implies a Type Distinction in the Halting Problem
Date: Sun, 11 May 2025 16:05:03 -0700
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Mr Flibble <flibble@red-dwarf.jmc.corp> writes:
> On Sun, 11 May 2025 18:15:47 +0100, Richard Heathfield wrote:
>
>> On 11/05/2025 17:59, Mr Flibble wrote:
>>> it is impossible to obtain a halting result
>> 
>> 
>> That sure looks like a concession that it's impossible to devise an
>> algorithm that will produce a halting result.
>> 
>> Well done. We got you there in the end.
>
> No. The reason why it is impossible to obtain a halting result for 
> pathological input is not the reason proposed by Turing (i.e. self-
> referential diagonalization), it is impossible to obtain a halting result 
> for pathological input because the self-referential conflation of decider 
> and input is a category error that prevents us from performing 
> diagonalization.

Is it possible to determine whether a given input is "pathological" or not?

> To usefully advance research in this area pathological input needs to be 
> excluded from the set of programs that can be analysed by a decider.

Can this exclusion be performed reliably and consistently?

-- 
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
void Void(void) { Void(); } /* The recursive call of the void */