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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Every D(D) simulated by H presents non-halting behavior to H
Date: Wed, 8 May 2024 08:01:54 -0500
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On 5/8/2024 3:59 AM, Mikko wrote:
> 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.
> 

*My fully operational code proves otherwise*

I seems like you guys don't have a clue about how infinite
recursion works. You can run the code and see that I am correct.

I have one concrete instance as fully operational code.
https://github.com/plolcott/x86utm/blob/master/Halt7.c
line 555 u32 HH(ptr P, ptr I) its input in on
line 932 int DD(int (*x)())
-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer