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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 14:08:46 -0500
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On 5/8/2024 11:07 AM, Mikko wrote:
> On 2024-05-08 13:01:54 +0000, olcott said:
> 
>> 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*
> 
> No, it doesn't.
> 
>> I seems like you guys don't have a clue about how infinite
>> recursion works.
> 
> Sure we know. It works so that the program that does it never
> returns and therefore is not any deider, and the calling
> program doesn't return, either, so it isn't a decider, either.
> 

*In other words you agree with this*
*In other words you agree with this*
*In other words you agree with this*

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 }

Any H/D pair matching the above template where D(D) is simulated
by the same H(D,D) that it calls cannot possibly reach past
it own line 03. Simple software engineering verified fact.

>>  You can run the code and see that I am correct.
> 
> Even without running the code it is clear that your "proves otherwise"
> is false.
> 
-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer