Re: Overview of proof that the input to HHH(DDD) specifies non-halting behavior --- Mike --- point by point

Op 13.aug.2024 om 17:25 schreef olcott:

On 8/13/2024 9:40 AM, Fred. Zwarts wrote:

Op 13.aug.2024 om 15:04 schreef olcott:

On 8/13/2024 5:57 AM, Mikko wrote:

On 2024-08-13 01:43:49 +0000, olcott said:
>

We prove that the simulation is correct.
Then we prove that this simulation cannot possibly
reach its final halt state / ever stop running without being aborted.
The semantics of the x86 language conclusive proves this is true.
>
Thus when we measure the behavior specified by this finite
string by DDD correctly simulated/emulated by HHH it specifies
non-halting behavior.
>
https://www.researchgate.net/ publication/369971402_Simulating_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D

>
Input to HHH(DDD) is DDD. If there is any other input then the proof is
not interesting.
>
The behviour specified by DDD on the first page of the linked article
is halting if HHH(DDD) halts. Otherwise HHH is not interesting.
>
Any proof of the false statement that "the input to HHH(DDD) specifies
non-halting behaviour" is either uninteresting or unsound.
>

>
void DDD()
{
   HHH(DDD);
   return;
}
>
It is true that DDD correctly emulated by any HHH cannot
possibly reach its own "return" instruction final halt state.

>
Contradiction in terminus.
A correct simulation is not possible.

 *YOU JUST DON'T GET THIS*
A simulation of N instructions of DDD by HHH according to
the semantics of the x86 language is stipulated to be correct.

You don't get that you cannot stipulate that something is correct. It must be proven. The semantics of the x86 language does not allow to use only the first N instructions of a halting program.

 *YOU JUST DON'T GET THIS EITHER*
A correct simulation of N instructions of DDD by HHH is
sufficient to correctly predict the behavior of an unlimited
simulation.

A false claim, without any evidence. HHH is stipulated to halt. So, when the simulation of HHH does not reach its final halt state, then the simulation failed. The unlimited simulation, e.g. by HHH1, shows that it halts.
But the aborting HHH cannot do an unlimited simulation of *itself*. Therefore it fails to reach the halting state. A failed simulation.
HHH cannot possible simulate itself correctly.

 *YOU JUST DON'T GET THIS EITHER*
Termination analyzers / halt deciders are only required
to correctly predict the behavior of their inputs.

You don't get that a prediction is incorrect when the input has halting behaviour and the prediction claims non-halting.

 *MOST JUST DON'T GET THIS*
Termination analyzers / halt deciders are only required
to correctly predict the behavior of their inputs, thus
the behavior of non-inputs is outside of their domain.

You don't get that DDD includes HHH. HHH is required to halt, so DDD halts as well. A correct prediction of this input would be that it halts. That can be done, e.g., by HHH1, but not by HHH itself.
You don't get that HHH cannot possibly simulate itself correctly.