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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: =?UTF-8?Q?Re=3A_Flibble=E2=80=99s_Leap=3A_Why_Behavioral_Divergence?=
 =?UTF-8?Q?_Implies_a_Type_Distinction_in_the_Halting_Problem?=
Date: Sun, 11 May 2025 20:48:46 -0500
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On 5/11/2025 8:13 PM, Richard Damon wrote:
> On 5/11/25 8:41 PM, olcott wrote:
>> On 5/11/2025 6:45 PM, Richard Damon wrote:
>>> On 5/11/25 7:14 PM, olcott wrote:
>>>> On 5/11/2025 6:05 PM, Keith Thompson wrote:
>>>>> Mr Flibble <flibble@red-dwarf.jmc.corp> writes:
>>>>>> On Sun, 11 May 2025 18:15:47 +0100, Richard Heathfield wrote:
>>>>>>
>>>>>>> On 11/05/2025 17:59, Mr Flibble wrote:
>>>>>>>> it is impossible to obtain a halting result
>>>>>>>
>>>>>>>
>>>>>>> That sure looks like a concession that it's impossible to devise an
>>>>>>> algorithm that will produce a halting result.
>>>>>>>
>>>>>>> Well done. We got you there in the end.
>>>>>>
>>>>>> No. The reason why it is impossible to obtain a halting result for
>>>>>> pathological input is not the reason proposed by Turing (i.e. self-
>>>>>> referential diagonalization), it is impossible to obtain a halting 
>>>>>> result
>>>>>> for pathological input because the self-referential conflation of 
>>>>>> decider
>>>>>> and input is a category error that prevents us from performing
>>>>>> diagonalization.
>>>>>
>>>>> Is it possible to determine whether a given input is "pathological" 
>>>>> or not?
>>>>>
>>>>>> To usefully advance research in this area pathological input needs 
>>>>>> to be
>>>>>> excluded from the set of programs that can be analysed by a decider.
>>>>>
>>>>> Can this exclusion be performed reliably and consistently?
>>>>>
>>>>
>>>> That is a good question. The answer is definitely
>>>> yes. When HHH emulates DDD it only needs to see
>>>> that DDD is calling itself with no conditional branch
>>>> instructions inbetween.
>>>>
>>>> Whether a function computed by a Turing machine can
>>>> do this is a different question.
>>>>
>>>
>>> So, try to do it.
>>>
>>
>> No need to. DDD emulated by HHH according to the
>> rules of the computational language that DD is
>> encoded within already proves that the HP
>> "impossible" input specifies a non-halting
>> sequence of configurations.
> 
> So, you are admitting you can't.
> 

I never admitted any such thing.
That I do not affirm that X is true
is not at all me affirming that X is false.

It is me trying to get you to focus on one
single point and not be scatterbrained all
over the place.

Prior to my work the answer for the halt status
of the HP's impossible input was: NO ONE KNOWS.
After my work the halt status becomes NON-HALTING.
This by itself is much more than anyone else
has ever accomplished with the HP.

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