Re: Halting Problem: What Constitutes Pathological Input

Am Mon, 05 May 2025 18:26:55 +0000 schrieb Mr Flibble:

On Mon, 05 May 2025 14:21:06 -0400, dbush wrote:

On 5/5/2025 2:14 PM, olcott wrote:

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.

 
In other words, you're claiming that there exists an algorithm, i.e. a
fixed immutable sequence of instructions, that neither halts nor does
not halt when executed directly.

 
It neither halts nor does not halt because it is predicated on a
category (type) error so it CANNOT be executed directly.

DD can most definitely be executed, and it halts.

Failure to do so in your next reply or within one hour of your next
posting in this newsgroup will be taken as your official on-the-record
admission that the halting problem is NOT ill-formed and that the below
criteria is VALID:

 
There is nothing to execute directly; if you try to by using a
simulating halt decider you get infinite recursion as a manifestation of
the category (type) error in the problem definition.

We have code for DD and a claimed HHH.

--
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.