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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.lang.c++,comp.lang.c
Subject: Re: Can you see that D correctly simulated by H remains stuck in
 recursive simulation?
Date: Sun, 26 May 2024 16:43:58 +0200
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Op 26.mei.2024 om 15:20 schreef olcott:
> On 5/26/2024 6:01 AM, Fred. Zwarts wrote:
>> Op 26.mei.2024 om 06:19 schreef olcott:
>>> On 5/25/2024 2:32 AM, Fred. Zwarts wrote:
>>>> Op 23.mei.2024 om 18:52 schreef olcott:
>>>>> 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.
>>>>>
>>>>
>>>> Olcott's own words are that the simulation of D never reaches past 
>>>> line 03. So the lines following line 03 do not play a role and, 
>>>> therefore, can be removed without changing the claim. This leads to:
>>>>
>>>> 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         return H(p, p);
>>>> 04       }
>>>> 05
>>>> 06       int main()
>>>> 07       {
>>>> 08         H(D,D);
>>>> 09         return 0;
>>>> 10       }
>>>>
>>>>
>>>> What we see is that the only property of D that is used is that it 
>>>> is a parameter duplicator. (Is that why it is called D?). H needs 2 
>>>> parameters, but it can be given only one input parameter, so the 
>>>> parameter duplicator is required to allow H to decide about itself.
>>>>
>>>>
>>>>
>>>> Of the infinite set of H that simulate at least one step, none of 
>>>> them, when simulated by H, halts, because none of them reaches its 
>>>> final state. Olcott's claim is equivalent to the claim of 
>>>> non-halting behaviour of H.
>>>> This means that a simulating halt-decider is a bad idea, because the 
>>>> decider itself does not halt.
>>>
>>> Not at all.
>>>     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.
>>>
>>>     This means that D cannot possibly reach its own line 06 and halt
>>>     in any finite steps of correct simulation. H is free to halt at
>>>     any time after these N finite steps of correct simulation.
>>>
>>>
>>
>> D does not reach it own line 04 because the simulation of H does not 
>> return to D. So, it shows that the simulation of H does not reach it 
>> final state, which proves that H does not halt.
> 
> Your transformation would have been acceptable if you retained the
> fact that H is a pure function that always halts and returns some value.
> 

Since H is required to halt, but H shows that H does not halt (because 
the simulation of H never reaches its final state), the conclusion must 
be that there is no such H.