Re: Halting Problem: What Constitutes Pathological Input

On 5/5/2025 11:42 AM, Mr Flibble wrote:

On Mon, 05 May 2025 10:51:40 -0500, 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;
}
>
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.
>
Thus the Halting Problem's "impossible" input is correctly determined to
be non-halting.

 Disagree: infinite recursion maps to incomputable rather than non-halting
and I reject that: it is not incomputable as the problem itself is ill-
formed due to a category (type) error.
 /Flibble

It is only ill-formed when construed in one of two ways:
(a) If D was actually able to do the opposite of
whatever value that H returns then it is ill-formed
because it is self-contradictory.
(b) If the problem is defined to have HHH report
on the direct execution of DD() then it is ill-formed
because HHH is required to report on different behavior
than its input DD actually specifies.
The call from the directly executed DD() to HHH(DD) returns.
The call from the correctly emulated DD() to HHH(DD)
CANNOT POSSIBLY RETURN. The directly executed HHH DOES RETURN.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer