Re: What is the best way for termination analyzers to handle pathological inputs?

On 6/10/25 3:05 PM, Mr Flibble wrote:

On Tue, 10 Jun 2025 14:53:47 -0400, Richard Damon wrote:
 

On 6/10/25 1:22 PM, olcott wrote:

On 6/10/2025 2:33 AM, Mikko wrote:

On 2025-06-09 21:14:58 +0000, olcott said:
>

The official "received view" of this is that the best we can possibly
do is to do nothing and give up.

>
There is no official view about "the best". What is the best depends
on what one needs and wants. Some may think that the best they can do
is to waste their life in trying to do the impossible.
>
>

It is not at all impossible to create a termination analyzer that
reports on the behavior specified by the input to HHH(DDD). It was
never correct to define a termination analyzer any other way.
>
>

Right, it is just a fact that it is impossible for HHH to be shuch a
analyzer.
>
A CORRECT Temrination analyzer of the input to HHH(DDD), that is to the
termination analysis of DDD, is to say it halts, since the HHH(DDD) that
DDD will call  will return non-halting to that DDD, and it will then
halt.

 But it will never "return" because it is infinitely recursive; the
simulation is aborted and a halting result if non-halting is returned
elsewhere.
 /Flibble

So, you have a problem, either you don't have a correct simulation to show you got the right answer, or you don't answer.
That is the problem with trying to have the decider itself be two contradictory entities.
A correct simulator can not be a correct decider it the input is actually non-halting.
There seems to be some mental block about the fact that the DEFINITION of this sort of decider is that:
H(M) returns 1 if UTM(M) halts, and
H(M) returns 0 if UTM(M) will never halt
If you try to combine the the UTM and H into one program that it can NEVER correctly return 0, as it can only return 0 if it never halt (and thus can't return a value)