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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Wed, 7 May 2025 15:44:12 -0500
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On 5/7/2025 3:25 PM, joes wrote:
> 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.
> 

If you examine 100% of ALL of the details
you will find that is counter-factual.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer