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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 19:41:06 -0500
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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.

This by itself is much more progress than anyone
else has ever made on the halting problem.

To the best of my recollection
Mike has already agreed that the outermost HHH
can dig into the details of all of the levels
of recursive simulation to get the details that
it currently uses. All of these details are
merely data to this outermost HHH.

This is analogous to a master UTM examining
all of its own tape, even those portions that
are allocated to slave UTMs.

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