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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 17:20:16 -0500
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On 5/24/2024 4:39 PM, olcott wrote:
> 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.
> 

I have learned from decades as a software engineer that complexity
is only manageable when it is isolated and minimized.

It is impossible to correctly understand termination analyzer H until
after one first has 100% perfectly complete and total understanding of
pure function simulator H/D pairs.

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