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From: olcott <polcott333@gmail.com>
Newsgroups: comp.lang.c++,comp.lang.c
Subject: Re: Can you see that D correctly simulated by H remains stuck in
 recursive simulation?
Date: Fri, 24 May 2024 12:03:04 -0500
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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.
>>
> 

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer