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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Tue, 6 May 2025 10:21:18 -0000 (UTC)
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Am Mon, 05 May 2025 13:07:27 -0500 schrieb olcott:
> On 5/5/2025 11:42 AM, Mr Flibble wrote:
>> On Mon, 05 May 2025 10:51:40 -0500, olcott wrote:
>>> On 5/5/2025 10:17 AM, Mr Flibble wrote:

>>>> What constitutes halting problem pathological input:
>>>> Input that would cause infinite recursion when using a decider of the
>>>> simulating kind.
>>>> Such input forms a category error which results in the halting
>>>> problem being ill-formed as currently defined.
>>>
>>> I prefer to look at it as a counter-example that refutes all of the
>>> halting problem proofs.

>>> When HHH computes the mapping from *its input* to the behavior of DD
>>> emulated by HHH this includes HHH emulating itself emulating DD. This
>>> matches the infinite recursion behavior pattern.
>>>
>>> Thus the Halting Problem's "impossible" input is correctly determined
>>> to be non-halting.
>> 
>> Disagree: infinite recursion maps to incomputable rather than
>> non-halting and I reject that: it is not incomputable as the problem
>> itself is ill- formed due to a category (type) error.
> 
> It is only ill-formed when construed in one of two ways:
> (a) If D was actually able to do the opposite of whatever value that H
> returns then it is ill-formed because it is self-contradictory.
D is actually able to be written assuming H exists. It does not contradict
itself but H.

> (b) If the problem is defined to have HHH report on the direct execution
> of DD() then it is ill-formed because HHH is required to report on
> different behavior than its input DD actually specifies.
>
> The call from the directly executed DD() to HHH(DD) returns. The call
> from the correctly emulated DD() to HHH(DD)
> CANNOT POSSIBLY RETURN. The directly executed HHH DOES RETURN.
Yes, HHH cannot simulate itself the same way as its direct execution.

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.