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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Mon, 5 May 2025 16:00:11 -0400
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In-Reply-To: <vvb52g$15u5b$6@dont-email.me>

On 5/5/2025 3:54 PM, olcott wrote:
> 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.
> 

In other words, you don't understand what the halting problem is about, 
because that is EXACTLY the question.

I want to know if any arbitrary algorithm X with input Y will halt when 
executed directly.  It would be *very* useful to me if I had an 
algorithm H that could tell me that in *all* possible cases.  If so, I 
could solve the Goldbach conjecture, among many other unsolved problems.

Does an algorithm H exist that can tell me that or not?