Re: Halting Problem: What Constitutes Pathological Input

On 5/5/2025 5:39 PM, olcott wrote:

On 5/5/2025 4:31 PM, dbush wrote:

On 5/5/2025 5:08 PM, olcott wrote:

On 5/5/2025 3:14 PM, dbush wrote:

On 5/5/2025 4:10 PM, olcott wrote:

On 5/5/2025 3:00 PM, dbush wrote:

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.
>

>
That question is in many textbooks yet is still
wrong because functions computed by models of
computation such as Turing Machines or RASP machines
are only allowed to use actual inputs as their basis.

>
And no Turing machine can compute the following mapping, as proven by Linz and other and as you have *explicitly* agreed is correct.
>

>
No TM can compute the square root of a dead rabbit either.

>
Strawman.  The square root of a dead rabbit does not exist, but the question of whether any arbitrary algorithm X with input Y halts when executed directly has a correct answer in all cases.
>

 It has a correct answer that cannot ever be computed

Excellent!  So you once again *explicitly* agree that the theorem that the halting problem proofs prove is correct.
I'll add this to the list of times you've admitted this for the next time you attempt to deny it.