Re: Halting Problem: What Constitutes Pathological Input

Am Tue, 06 May 2025 10:23:18 -0500 schrieb olcott:

On 5/6/2025 4:30 AM, Mikko wrote:

On 2025-05-05 19:27:18 +0000, olcott said:

On 5/5/2025 2:12 PM, dbush wrote:

On 5/5/2025 2:47 PM, olcott wrote:

On 5/5/2025 1:21 PM, 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.
>

That is not what I said.

>
Then there's no category error, and the halting function is well
defined.  It's just that no algorithm can compute it.

>
It is insufficiently defined thus causing it to be incoherently
defined.

 
It is well defined. There are computations that halt and computations
that do not. Nothing else is in the scope of the halting problem.
 

It is incorrectly defined when-so-ever it is not specified that a
specific sequence of steps must be applied to the input to derive the
output.
That DD() halts therefore I guess that DD correctly emulated by HHH must
halt too IS NOT A SPECIFIC SEQUENCE OF STEPS.
It is merely an incorrect guess.

Oh wow. As a simulator, HHH must produce the same behaviour as the direct
execution.

--
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.