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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 10:40:42 -0500
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On 5/7/2025 3:57 AM, Mikko wrote:
> On 2025-05-06 15:36:00 +0000, olcott said:
> 
>> 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.
> 
> No, that is not what the halting problem requires. The halting problem
> requires that HHH must be given a finite string that tells what HHH
> needs to know about DD in order to correctly predict whether DD halts
> if it is directly executed.
> 

And for the same reason
<sarcasm>
int sum(int x, int y) { return x + y; }
sum(3,2) must report on the sum of 5 + 6
and is not allowed to report on the sum of 3 + 2.

This is because Truth is a Democracy and the common
misconceptions cast more votes than correct analysis.
</sarcasm>



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