Re: DD simulated by HHH cannot possibly halt (Halting Problem)

On 4/5/2025 2:42 AM, Richard Heathfield wrote:

On 05/04/2025 07:14, olcott wrote:

On 4/4/2025 10:49 PM, Richard Heathfield wrote:

On 05/04/2025 00:41, olcott wrote:

*Simulating termination analyzer Principle*
It is always correct for any simulating termination
analyzer to stop simulating and reject any input that
would otherwise prevent its own termination. The
only rebuttal to this is rejecting the notion that
deciders must always halt.

>

>
typedef void (*ptr)();
int HHH(ptr P);
>
int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}
>
int main()
{
   HHH(DD);
}
>

In other words, you operate on the principle that deciders don't have to (and indeed can't) always make a correct decision on whether an input program halts.
>

>
The termination analyzer HHH would be correct
to determine that it must stop simulating DD to
prevent its own non-termination

 Fine, but then it fails to do its job. What you are learning (albeit slowly) is that the termination analyser HHH can't analyse whether DD terminates. It is therefore not a general purpose termination analyser.
 

Introduction to the Theory of Computation 3rd Edition
by Michael Sipser (Author) (best selling textbook)
<MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
     If simulating halt decider H correctly simulates its input D
     until H correctly determines that its simulated D would never
     stop running unless aborted then
     H can abort its simulation of D and correctly report that D
     specifies a non-halting sequence of configurations.
</MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
*DERIVES THIS PARAPHRASE*
*Simulating termination analyzer Principle*
It is always correct for any simulating termination
analyzer to stop simulating and reject any input that
would otherwise prevent its own termination. The
only rebuttal to this is rejecting the notion that
deciders must always halt.
It is self-evident that DD simulated by HHH is an
instance of the above therefore HHH is correct to
reject DD as non-halting.

Your reasoning is that it has a good excuse and can be forgiven for failing. Fine, but it still fails. Calling an abort 'correct' doesn't stop it being an abort.
 

--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer