Re: Halting Problem: What Constitutes Pathological Input

Op 06.mei.2025 om 04:29 schreef olcott:

On 5/5/2025 8:06 PM, Richard Damon wrote:

On 5/5/25 11:51 AM, olcott wrote:

On 5/5/2025 10:17 AM, Mr Flibble wrote:

What constitutes halting problem pathological input:
>
Input that would cause infinite recursion when using a decider of the
simulating kind.
>
Such input forms a category error which results in the halting problem
being ill-formed as currently defined.
>
/Flibble

>
I prefer to look at it as a counter-example that refutes
all of the halting problem proofs.
>
int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}

>
Which isn't a program until you include the SPECIFIC HHH that it refutes, and thus your talk about correctly emulated by HHH is just a lie.
>

>
https://github.com/plolcott/x86utm
>
The x86utm operating system includes fully
operational HHH and DD.
https://github.com/plolcott/x86utm/blob/master/Halt7.c
>
When HHH computes the mapping from *its input* to
the behavior of DD emulated by HHH this includes
HHH emulating itself emulating DD. This matches
the infinite recursion behavior pattern.
>

>
And *ITS INPUT*, for the HHH that answers 0, is the representation of a program

 Not at all. This has always been stupidly wrong.
The input is actually a 100% perfectly precise
sequence of steps. With pathological self-reference
some of these steps are inside the termination analyzer.
 

Your system seems to have a problem with defining the meaning of the word 'self'. There is no self-reference in a correct decider. If the programmer of HHH introduced a self-reference (e.g., by including the address of HHH), then that is an error of the programmer, not of the counter example in the Linz proof, where H and embedded_h are not the same thing (and can be different as long a embedded_H returns the same as H) and so there is no self-reference in the proof.