Re: Halting Problem: What Constitutes Pathological Input

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:
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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

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Or to put it another way, the answer is undecidable, QED.
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See? You got there in the end.
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Is this sentence true or false: "What time is it?"
is also "undecidable" because it is not a proposition
having a truth value.
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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.
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Can Carol correctly answer “no” to this (yes/no) question?
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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.

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And "does algorthm X with input Y halt when executed directly" has a single well defined answer.
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That is not even the actual question.
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Does the finite string input DD to HHH specify
a computation that halts? No it does not.

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That question is a category error. The halting question is not about
finite strings but about computations.

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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