Re: Halting Problem: What Constitutes Pathological Input

On 5/7/25 11:40 AM, olcott wrote:

On 5/7/2025 3:57 AM, Mikko wrote:

On 2025-05-06 15:36:00 +0000, olcott said:
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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.

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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.
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 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>
  

No, but that is exactly the logic that you HHH uses, It presumes the input calls a version of HHH that it doesn't, and thus answers about an input that it wasn't actually given.