Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Why Peter Olcott is both right and wrong
Date: Fri, 16 May 2025 09:38:02 +0300
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On 2025-05-15 13:03:19 +0000, Mr Flibble said:

> On Thu, 15 May 2025 11:07:48 +0300, Mikko wrote:
> 
>> On 2025-05-15 06:27:13 +0000, Mr Flibble said:
>> 
>>> Peter is right to say that the halting problem as defined is flawed: he
>>> agrees with me that there is category error at the heart of the problem
>>> definition whereby the decider is conflated with the program being
>>> analysed in an ill-formed self-referential dependency that manifests in
>>> his simulating halt decider as "aborted" infinite recursion.
>> 
>> No, he is not right about that. There is no flaw about the problem. The
>> problem is to create a halt decider. Every Turing machine either is or
>> is not a halt decider. In order to demonstrate that a Turing machine is
>> not a halt decider it is sufficient to show one example that it does not
>> determine correctly.
> 
> False -- the pathologial input cannot be determined correctly because it
> is ill-posed.

Olcott's "pathological" inputa are not "ill-posed". They are well defined
programs that can be run, and have been, and they halt when run.

-- 
Mikko