Re: Halting Problem: What Constitutes Pathological Input

Am Mon, 05 May 2025 13:14:25 -0500 schrieb olcott:

On 5/5/2025 11:16 AM, dbush wrote:

On 5/5/2025 12:13 PM, Mr Flibble wrote:

On Mon, 05 May 2025 11:58:50 -0400, dbush wrote:

On 5/5/2025 11:51 AM, olcott wrote:

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.
>

Which is a contradiction.  Therefore the assumption that the above
mapping is computable is proven false, as Linz and others have proved
and as you have *explicitly* agreed is correct.

>
The category (type) error manifests in all extant halting problem
proofs including Linz.  It is impossible to prove something which is
ill-formed in the first place.

 
All algorithms either halt or do not halt when executed directly.
Therefore the problem is not ill formed.
 

When BOTH Boolean RETURN VALUES are the wrong answer THEN THE PROBLEM IS
ILL-FORMED. Self-contradiction must be screened out as semantically
incorrect.
>

You only get something that appears that way when a false assumption is
made, namely that the halting function is computable.

The mapping from the input HHH(DD) finite string of machine code to DOES
SPECIFY RECURSIVE EMULATION THAT WOULD PREVENT DD FROM EVER HALTING.

...when simulated by HHH. Yes, it cannot simulate DD or itself correctly.

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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.