Re: Can you see that D correctly simulated by H remains stuck in recursive simulation?

On 25/05/2024 08:32, Fred. Zwarts wrote:

Op 23.mei.2024 om 18:52 schreef olcott:

typedef int (*ptr)();  // ptr is pointer to int function in C
00       int H(ptr p, ptr i);
01       int D(ptr p)
02       {
03         int Halt_Status = H(p, p);
04         if (Halt_Status)
05           HERE: goto HERE;
06         return Halt_Status;
07       }
08
09       int main()
10       {
11         H(D,D);
12         return 0;
13       }
>
The above template refers to an infinite set of H/D pairs where D is
correctly simulated by pure function H. This was done because many
reviewers used the shell game ploy to endlessly switch which H/D was
being referred to.
>
*Correct Simulation Defined*
This is provided because every reviewer had a different notion of
correct simulation that diverges from this notion.
>
In the above case a simulator is an x86 emulator that correctly emulates
at least one of the x86 instructions of D in the order specified by the
x86 instructions of D.
>
This may include correctly emulating the x86 instructions of H in the
order specified by the x86 instructions of H thus calling H(D,D) in
recursive simulation.
>
*Execution Trace*
Line 11: main() invokes H(D,D); H(D,D) simulates lines 01, 02, and 03 of
D. This invokes H(D,D) again to repeat the process in endless recursive
simulation.
>

 Olcott's own words are that the simulation of D never reaches past line 03. So the lines following line 03 do not play a role and, therefore, can be removed without changing the claim. This leads to:
 typedef int (*ptr)();  // ptr is pointer to int function in C
00       int H(ptr p, ptr i);
01       int D(ptr p)
02       {
03         return H(p, p);
04       }
05
06       int main()
07       {
08         H(D,D);
09         return 0;
10       }
 

Correct - as far as this specific thread is concerned.  But PO's H and P are intended to be part of a larger argument supposedly refuting the standard halting problem (HP) proof (that no TM is a halt decider), e.g. as covered in the Linz book.  PO has created an extract of that proof as a PDF that he sometimes links to.
Also note that PO's claim (in this specific thread) is that the *simulation* of D never reaches past line 03.  That is not saying that the *computation* D(D) never proceeds past line 3 or that D(D) never halts.  (This is important in the wider HP proof context.  PO is deeply confused on this point.)

 What we see is that the only property of D that is used is that it is a parameter duplicator. (Is that why it is called D?). H needs 2 parameters, but it can be given only one input parameter, so the parameter duplicator is required to allow H to decide about itself.

Yes, but the rest of D is the key to its role in the HP proof - again, not relevant for this specific thread.  [In HP proof, D's role is to calculate H's decision on whether D(D) halts and then behave in the opposite fashion, providing a counterexample to the claim that H correctly decides the halting behaviour of /all/ inputs (P,I).  I.e. it shows that H gets it wrong for the case P=I=D.]

   Of the infinite set of H that simulate at least one step, none of them, when simulated by H, halts, because none of them reaches its final state. Olcott's claim is equivalent to the claim of non-halting behaviour of H.

No - note my remarks above about the distinction between the behaviour of the *computation* D(D) and the (partial) *simulation* of that computation by H.  H can simply choose to discontinue that simulation at any point [aka "abort" the simulation, in PO's terms], but then H would continue and halt.
PO is pretty clueless about everything involved, and I believe he is quite incapable of abstract thought, including what people would generally regard as "logical reasoning", so there really is no point in arguing with him.  (I mean Really...)
Mike.