Re: Halting Problem: What Constitutes Pathological Input

Am Mon, 05 May 2025 10:51:40 -0500 schrieb olcott:

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.

 
I prefer to look at it as a counter-example that refutes all of the
halting problem proofs.
 
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.

It is supposed to map to the direct execution in order for it to be a
simulator.

Thus the Halting Problem's "impossible" input is correctly determined to
be non-halting.

Making the direct execution halt, which it actually does, in line with
Turing's proof.

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.