Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT

On 29/04/2025 22:44, olcott wrote:

On 4/29/2025 3:23 PM, Richard Heathfield wrote:

On 29/04/2025 20:57, olcott wrote:

On 4/29/2025 10:33 AM, Fred. Zwarts wrote:

>
<snip>
>

makes it impossible for H to see the behaviour of P(D).
The behaviour of P(D) does not change, but H does not see it.

>
H MUST REPORT ON THE BEHAVIOR THAT IT DOES SEE

>
H has the whole P tape and the whole D tape at its disposal. There is nothing it can't inspect.
>

 int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}
 When P has a pathological relationship
to H, the input to H(P,D) DOES NOT HALT.

Presumably you mean that the Turing machine on tape P, given tape D as input, doesn't halt.
But if that's true, then we can construct a pathological meta-P, so to speak, and arrange it so that it /does/ halt. When we feed /that/ to your HHH, it will now give the wrong answer.

Not being able to see how P behaves in simulation is no excuse for getting the answer wrong.

 THEN...
I am thinking of the sum of two integers
not telling you what these integers are
is no excuse for you not providing their correct sum.

Absolutely.
 From my perspective, with the information I have available, I must fail to complete the task, because the answer is incomputable.
Similarly, we cannot write an H that, given arbitrary P and D, always correctly reports on whether feeding D to P would result in P halting. It can't be done. It's incomputable. That's the whole point!
The parallel is not /quite/ perfect, though, because H can see the tapes (P and D), and can examine them in their entirety.
Unfortunately, this isn't enough. We still can't guarantee to deduce whether P(D) would halt.

If because of limitations in H it fails to spot behaviour that would have changed its report on P(D), that just means that H is broken.
>
But don't bother trying to fix it. Turing has already proved that you can't.
>

 You are simply not bothering to pay complete attention.

I'm ignoring most of your nonsense, if that's what you mean.
What you're ignoring is mathematical rigour.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within