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

On 5/24/2024 8:37 AM, David Brown wrote:

On 24/05/2024 15:08, olcott wrote:

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.

 No, it does not.
 As Richard says, you have main -> H -> D -> H -> ...
 For any finite system, you will run out of stack space.  This is undefined behaviour in C.  /Anything/ can happen - including halting, returning a halt status of 1, or a halt status of 0, or a not halting, or printing out the works of Shakespeare.  Or it could cause the program to jump directly to line 6.  Once you hit undefined behaviour, you cannot prove /anything/.
 

Abnormal termination does not count as halting.
The software engineering equivalent of the theory of computation
term: D {halts} is D {terminates normally}.

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.
>

 

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Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
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