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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Wed, 7 May 2025 20:25:04 -0000 (UTC)
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Am Tue, 06 May 2025 10:23:18 -0500 schrieb olcott:
> On 5/6/2025 4:30 AM, Mikko wrote:
>> On 2025-05-05 19:27:18 +0000, olcott said:
>>> On 5/5/2025 2:12 PM, dbush wrote:
>>>> On 5/5/2025 2:47 PM, olcott wrote:
>>>>> On 5/5/2025 1:21 PM, dbush wrote:
>>>>>> On 5/5/2025 2:14 PM, olcott wrote:
>>>>>>> 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.
>>>>>>
>>>>>> In other words, you're claiming that there exists an algorithm,
>>>>>> i.e. a fixed immutable sequence of instructions, that neither halts
>>>>>> nor does not halt when executed directly.
>>>>>>
>>>>> That is not what I said.
>>>>
>>>> Then there's no category error, and the halting function is well
>>>> defined.  It's just that no algorithm can compute it.
>>>
>>> It is insufficiently defined thus causing it to be incoherently
>>> defined.
>> 
>> It is well defined. There are computations that halt and computations
>> that do not. Nothing else is in the scope of the halting problem.
>> 
> It is incorrectly defined when-so-ever it is not specified that a
> specific sequence of steps must be applied to the input to derive the
> output.
> That DD() halts therefore I guess that DD correctly emulated by HHH must
> halt too IS NOT A SPECIFIC SEQUENCE OF STEPS.
> It is merely an incorrect guess.
Oh wow. As a simulator, HHH must produce the same behaviour as the 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.