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

On 30/04/2025 16:15, olcott wrote:

On 4/29/2025 5:03 PM, Richard Heathfield wrote:

On 29/04/2025 22:38, olcott wrote:
>
<snip>
>

>
int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}
>
HHH is correct DD as non-halting BECAUSE THAT IS
WHAT THE INPUT TO HHH(DD) SPECIFIES.

>
You're going round the same loop again.
>
Either your HHH() is a universal termination analyser or it isn't.

 The domain of HHH is DD.

Then it is attacking not the Halting Problem but the Olcott Problem, which is of interest to nobody but you.

 

If it isn't, it's irrelevant to the Halting Problem,

 It correctly refutes the conventional proof of the
Halting Problem proofs.

No, it doesn't. To do that, you would have to devise a program to correctly analyse *any* of *all* possible programs, given any of *all* possible inputs.
When you've achieved that, let me know, and I'll show you how to overturn the 'refutation' by constructing a program that your program can't handle.

The "impossible" input specifies
non-halting behavior and the contradictory part of DD
is unreachable code.

It's not an impossible input. There's nothing impossible about being able to analyse /one/ program in line with your expectations. The impossibility comes from HHH being able to correctly determine halting behaviour for *any* program (although I would grant that the program can at least be expected to be syntactically correct).

Have you ever done any actual programming?

No, mate. I paint potatoes. There's good money in spud daubs.
Have you ever done any actual reading for comprehension? The Halting Problem doesn't require you to devise a program to analyse just DD. It requires you to devise a program to correctly analyse *any* of *all* possible programs, given any of *all* possible inputs. You have admitted that your HHH doesn't do that. It therefore has nothing relevant to say about the Halting Problem.
<snip>
--
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