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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Mon, 5 May 2025 17:19:50 -0500
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On 5/5/2025 5:03 PM, dbush wrote:
> On 5/5/2025 5:47 PM, olcott wrote:
>> On 5/5/2025 4:40 PM, Richard Heathfield wrote:
>>> On 05/05/2025 22:31, dbush wrote:
>>>> On 5/5/2025 5:08 PM, olcott wrote:
>>>
>>> <snip>
>>>
>>>>> No TM can compute the square root of a dead rabbit either.
>>>>
>>>> Strawman.  The square root of a dead rabbit does not exist,
>>>
>>> Don't be so sure. I have several on my mantelpiece and two more on 
>>> order. For once, olcott is right; there is no way to compute them. 
>>> They do, however, need thorough and regular polishing. Black polish 
>>> or brown? Well, that's undecidable.
>>>
>>>> but the question of whether any arbitrary algorithm X with input Y 
>>>> halts when executed directly has a correct answer in all cases.
>>>
>>> Indeed it has.
>>>
>>>> It's just that no algorithm exists that can compute that mapping, as 
>>>> proven by Linz and other and as you have *explicitly* agreed is 
>>>> correct.
>>>
>>> He's coming round to the idea, albeit slowly. He can't bring himself 
>>> to describe the mapping as 'incomputable' or 'undecidable', but he's 
>>> started to claim that such a mapping is 'incorrect', which is a tacit 
>>> acknowledgement that it exists.
>>>
>>
>> When the input to HHH(DD) is mapped to the
>> behavior that this input actually specifies
>> IT DOES NOT HALT.
>>
> 
> In other words, HHH doesn't meet the requirements to be a solution to 
> the halting problem:
> 

A deeper understanding proves that those requirements
contradict basic axioms of computer science.

People that think that computer science textbooks
are the infallible word of God will never get this.

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