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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Tue, 6 May 2025 10:36:00 -0500
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On 5/6/2025 4:47 AM, Mikko wrote:
> On 2025-05-05 19:54:55 +0000, olcott said:
> 
>> On 5/5/2025 2:49 PM, dbush wrote:
>>> On 5/5/2025 3:38 PM, olcott wrote:
>>>> On 5/5/2025 2:23 PM, Richard Heathfield wrote:
>>>>> On 05/05/2025 20:20, olcott wrote:
>>>>>> Is "halts" the correct answer for H to return?  NO
>>>>>> Is "does not halt" the correct answer for H to return?  NO
>>>>>> Both Boolean return values are the wrong answer
>>>>>
>>>>> Or to put it another way, the answer is undecidable, QED.
>>>>>
>>>>> See? You got there in the end.
>>>>>
>>>>
>>>> Is this sentence true or false: "What time is it?"
>>>> is also "undecidable" because it is not a proposition
>>>> having a truth value.
>>>>
>>>> Is this sentence true or false: "This sentence is untrue."
>>>> is also "undecidable" because it is not a semantically sound
>>>> proposition having a truth value.
>>>>
>>>> Can Carol correctly answer “no” to this (yes/no) question?
>>>>
>>>> Both Yes and No are the wrong answer proving that
>>>> the question is incorrect when the context of who
>>>> is asked is understood to be a linguistically required
>>>> aspect of the full meaning of the question.
>>>
>>> And "does algorthm X with input Y halt when executed directly" has a 
>>> single well defined answer.
>>>
>>
>> That is not even the actual question.
>>
>> Does the finite string input DD to HHH specify
>> a computation that halts? No it does not.
> 
> That question is a category error. The halting question is not about
> finite strings but about computations.
> 

HHH must compute the mapping from its finite string
of x86 code input to the actual behavior that this
finite string input specifies.

The same thing goes for TM's
H must compute the mapping from the finite string
TM source-code input to the behavior that this TM
source-code specifies.

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