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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Can you see that D correctly simulated by H remains stuck in
 recursive simulation?
Date: Thu, 23 May 2024 21:44:43 -0400
Organization: i2pn2 (i2pn.org)
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On 5/23/24 1:04 PM, 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 pair
> 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.
> 
>     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.
> 

Questions:

By your definiton of "Correct Simulation", you do realize that you have 
broken connection between the simulaiton not completing and the program 
described by the input not halting?

Also, you do realize that by your requirement on H just being a "pure 
function" that does NOT say that you H qualified to be the computational 
equivalent for a Turing Machine?

That due to your "strange" definition of what D is, you are putting 
yourself outside of the grounds of "Computation Theory", as that deals 
with the behavior of specific PROGRAMS, and not the "Program Templates" 
like your D, our the "Infinite set of H/D pairs"?

Also, your "templagte D" is NOT built per either the Linz or Sipser 
rules, as both of those had D built with a COPY of H, which is one of 
your problems with a "Pure Function" as the equivelent. You have shown 
that your H fails to meet the requirements of a Turing Machine 
equivalent, as you can't (or it seems you can't) make equivalent copies, 
where all copies always give the same answer for the same inputs. This 
is a fundamental property of Turing Machines, which is why just bing a 
"Pure Function" isn't good enough.

These issus need to be handled or acknowledged, before agreement on your 
question, as you have shown a history of taking a statement and twisting 
it (perhaps not intentionally, but because you don't understand what was 
being communicated) so we need to have a firm understand of what you 
mean and evidence that you accept the limititation causes by your 
altered definitions from the problem that you initially claimed to have 
started on.

Of course, it also means that even if/when you get your agreement, you 
are no closer to your halting proof, as you have shown that you 
undestand that you conditions actually tell you NOTHING about the actual 
behavior of halting.