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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Can you see that D correctly simulated by H remains stuck in
 recursive simulation?
Date: Fri, 24 May 2024 16:39:03 -0500
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On 5/24/2024 4:03 PM, Richard Damon wrote:
> On 5/24/24 4:01 PM, olcott wrote:
>> On 5/24/2024 12:25 PM, Richard Damon wrote:
>>> On 5/24/24 1:10 PM, olcott wrote:
>>>> On 5/24/2024 2:37 AM, Fred. Zwarts wrote:
>>>>> Op 23.mei.2024 om 19:04 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 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.
>>>>>>
>>>>>
>>>>> Of course this depends very much on the exact meaning of 'correct 
>>>>> simulation', or 'correctly emulating'. 
>>>>
>>>> Not when these are defined above.
>>>>
>>>>> E.g., take the call to H(p, p). If H recognizes that it is a call 
>>>>> to a H with the same algorithm as is it using itself, and it knows 
>>>>> that itself returns a certain integer value K, than it can be 
>>>>> argued that it is a correct emulation to substitute the call to H 
>>>>> with this integer value K, which is assigned to Halt_Status. Then 
>>>>> the simulation of D can proceed to line 04.
>>>>> What we need is an exact definition of 'correct simulation', in this 
>>>>
>>>> No, you simply need to pay complete attention to the fact that this
>>>> has already been provided.
>>>>
>>>> I have been over the exact same issue with dozens and dozen of people
>>>> though hundreds and hundreds of messages over two years.
>>>
>>> Excpet that we have two contradictory definitions present, 
>>
>> Yes you have a definition of simulation where the x86 machine
>> language of D is simulated incorrectly or in the wrong order.
> 
> Nope. The UTM definition still simulates EVERY x86 machine language 
> instruction of D simulated correctly in the exact order. The added 
> requirement is that we look at a simulation that is never aborted.

H is a pure function that always returns 56 at some point other
than that H is isomorphic to a UTM.

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