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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 11:46:33 +0300
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On 2024-05-07 15:40:32 +0000, olcott said:

> 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).

No, it does not. D does not know which H simulates it or even whther is
simulated at all. D calls the one whose name is H. The association of D
with the H of the same pair, if desired, must be done outside of D.

-- 
Mikko