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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Can you see that D correctly simulated by H remains stuck in
 recursive simulation?
Date: Fri, 24 May 2024 07:14:05 -0400
Organization: i2pn2 (i2pn.org)
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On 5/24/24 5:03 AM, Mikko wrote:
> On 2024-05-23 17:04:49 +0000, olcott said:
> 
>> 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.
> 
> One can see that D is never stuch in recursive simulation unless H is.
> Whether H is cannot be seen has the details of H are not shown. Even
> if they were H must, in order to simulate any x86 execution, be so
> big and complicated that essential aspect may be hard to see; depending,
> of course, on how the code is organized.
> 

Yep, that is a key part of the issue.

We could say that his H proves that his H isn't a decider, because it 
isn't a "Halting Program" for the input.