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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory,sci.logic
Subject: Re: Every D(D) simulated by H presents non-halting behavior to H ###
Date: Tue, 28 May 2024 11:21:21 +0200
Organization: A noiseless patient Spider
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Op 27.mei.2024 om 17:43 schreef olcott:
> On 5/27/2024 9:58 AM, Richard Damon wrote:
>> On 5/27/24 10:39 AM, 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 either pure simulator H or 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 many reviewers had a different notion of
>     correct simulation that diverges from this notion.
> 
>     A simulator is an x86 emulator that correctly emulates 1 to N of the
>     x86 instructions of D in the order specified by the x86 instructions
>     of D. This may include M recursive emulations of H emulating itself
>     emulating D.
> 
> When we see that D correctly simulated by pure simulator H would remain
> stuck in infinite recursive simulation then we also know that less than
> an infinite number of steps is not enough steps for D correctly
> simulated by pure function H to reach its own simulated final state at
> line 06 and halt.
> 

We can equally well replace D with H.

When we see that H correctly simulated by pure simulator H would remain
stuck in infinite recursive simulation then we also know that less than
an infinite number of steps is not enough steps for H correctly
simulated by pure function H to reach its own simulated final state and 
halt.