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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 10:17:19 -0000 (UTC)
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Am Mon, 05 May 2025 13:14:25 -0500 schrieb olcott:
> On 5/5/2025 11:16 AM, dbush wrote:
>> On 5/5/2025 12:13 PM, Mr Flibble wrote:
>>> On Mon, 05 May 2025 11:58:50 -0400, dbush wrote:
>>>> On 5/5/2025 11:51 AM, olcott wrote:

>>>>> 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.
>>>>>
>>>> Which is a contradiction.  Therefore the assumption that the above
>>>> mapping is computable is proven false, as Linz and others have proved
>>>> and as you have *explicitly* agreed is correct.
>>>
>>> The category (type) error manifests in all extant halting problem
>>> proofs including Linz.  It is impossible to prove something which is
>>> ill-formed in the first place.
>> 
>> All algorithms either halt or do not halt when executed directly.
>> Therefore the problem is not ill formed.
>> 
> When BOTH Boolean RETURN VALUES are the wrong answer THEN THE PROBLEM IS
> ILL-FORMED. Self-contradiction must be screened out as semantically
> incorrect.
>
>> You only get something that appears that way when a false assumption is
>> made, namely that the halting function is computable.
> The mapping from the input HHH(DD) finite string of machine code to DOES
> SPECIFY RECURSIVE EMULATION THAT WOULD PREVENT DD FROM EVER HALTING.
....when simulated by HHH. Yes, it cannot simulate DD or itself correctly.

-- 
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.