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

Op 24.mei.2024 om 15:08 schreef olcott:

On 5/24/2024 7:10 AM, Richard Harnden wrote:

On 23/05/2024 17:52, olcott wrote:

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.

>
>
So, you have: main -> H -> D -> H -> D -> ... -> H -> D until you run out of stack?
>
No return statement is ever reached.
Line 3 never completes.
Halt_Status at line 3 never gets a value.
>
</shrug>
>
>

Thanks.
 Proving that D correctly simulated by H never reaches its final
state at line 06 and halts. Thus proving that the halting problem's
counter-example input D would be correctly determined to be non-halting
by its simulating termination analyzer H.
 

No. If true, it proves that no simulation is able to correctly determine the halting status of D, because simulations are not even able to simulate one line of D.