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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: Tue, 7 May 2024 21:40:19 -0500
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On 5/7/2024 9:36 PM, Richard Damon wrote:
> On 5/7/24 11:40 AM, olcott wrote:
>> 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
> 
> Ok, and I can make an H that simulates its D to the final state.

Liar

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