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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Every D(D) simulated by H presents non-halting behavior to H
Date: Wed, 8 May 2024 11:59:25 +0300
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On 2024-05-07 19:05:54 +0000, olcott said:

> On 5/7/2024 1:54 PM, Fred. Zwarts wrote:
>> Op 07.mei.2024 om 17:40 schreef olcott:
>>> On 5/7/2024 6:18 AM, Richard Damon wrote:
>>>> On 5/7/24 3:30 AM, Mikko wrote:
>>>>> On 2024-05-06 18:28:37 +0000, olcott said:
>>>>> 
>>>>>> On 5/6/2024 11:19 AM, Mikko wrote:
>>>>>>> On 2024-05-05 17:02:25 +0000, olcott said:
>>>>>>> 
>>>>>>>> The x86utm operating system: https://github.com/plolcott/x86utm enables
>>>>>>>> one C function to execute another C function in debug step mode.
>>>>>>>> Simulating Termination analyzer H simulates the x86 machine code of its
>>>>>>>> input (using libx86emu) in debug step mode until it correctly matches a
>>>>>>>> correct non-halting behavior pattern proving that its input will never
>>>>>>>> stop running unless aborted.
>>>>>>>> 
>>>>>>>> Can D correctly simulated by H terminate normally?
>>>>>>>> 00 int H(ptr x, ptr x)  // ptr is pointer to int function
>>>>>>>> 01 int D(ptr x)
>>>>>>>> 02 {
>>>>>>>> 03   int Halt_Status = H(x, x);
>>>>>>>> 04   if (Halt_Status)
>>>>>>>> 05     HERE: goto HERE;
>>>>>>>> 06   return Halt_Status;
>>>>>>>> 07 }
>>>>>>>> 08
>>>>>>>> 09 int main()
>>>>>>>> 10 {
>>>>>>>> 11   H(D,D);
>>>>>>>> 12 }
>>>>>>>> 
>>>>>>>> *Execution Trace*
>>>>>>>> Line 11: main() invokes H(D,D);
>>>>>>>> 
>>>>>>>> *keeps repeating* (unless aborted)
>>>>>>>> Line 03: simulated D(D) invokes simulated H(D,D) that simulates D(D)
>>>>>>>> 
>>>>>>>> *Simulation invariant*
>>>>>>>> D correctly simulated by H cannot possibly reach past its own line 03.
>>>>>>>> 
>>>>>>>> The above execution trace proves that (for every H/D pair of the
>>>>>>>> infinite set of H/D pairs) each D(D) simulated by the H that this D(D)
>>>>>>>> calls cannot possibly reach past its own line 03.
>>>>>>> 
>>>>>>> When you say "every H/D pair" you should specify which set of pairs
>>>>>>> you are talking about. As you don't, your words don't mean anything.
>>>>>>> 
>>>>>> 
>>>>>> Every H/D pair in the universe where D(D) is simulated by the
>>>>>> same H(D,D) that D(D) calls. This involves 1 to ∞ steps of D
>>>>>> and also includes zero to ∞ recursive simulations where H
>>>>>> H simulates itself simulating D(D).
>>>>> 
>>>>> "In the universe" is not a set. In typical set theories like ZFC there
>>>>> is no universal set.
>>>> 
>>> 
>>> This template defines an infinite set of finite string H/D pairs where 
>>> each D(D) that is simulated by H(D,D) also calls this same H(D,D).
>>> 
>>> These H/D pairs can be enumerated by the one to ∞ simulated steps of D 
>>> and involve zero to ∞ recursive simulations of H simulating itself 
>>> simulating D(D). Every time Lines 1,2,3 are simulated again defines
>>> one more level of recursive simulation.
>>> 
>>> 1st element of H/D pairs 1 step  of D  is simulated by H
>>> 2nd element of H/D pairs 2 steps of D are simulated by H
>>> 3rd element of H/D pairs 3 steps of D are simulated by H
>>> 
>>> 4th element of H/D pairs 4 steps of D are simulated by H
>>> this begins the first recursive simulation at line 01
>>> 
>>> 5th element of H/D pairs 5 steps of D are simulated by
>>> next step of the first recursive simulation at line 02
>>> 
>>> 6th element of H/D pairs 6 steps of D are simulated by
>>> last step of the first recursive simulation at line 03
>>> 
>>> 7th element of H/D pairs 7 steps of D are simulated by H
>>> this begins the second recursive simulation at line 01
>> 
>> Is this the definition of the infinite set of H? We can think of many 
>> more simulations that only these.
> 
> This template defines an infinite set of finite string H/D pairs where
> each D(D) that is simulated by H(D,D) also calls this same H(D,D).
> 
> No-one can possibly show one element of this set where D(D) reaches
> past its own line 03.

If H is a decider of any kind then the D build from it reaches its line
4 as numberd above. Whether the simulation of D by H reaches that line
is another question.

-- 
Mikko