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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Every D(D) simulated by H presents non-halting behavior to H ###
Date: Thu, 9 May 2024 22:31:24 -0400
Organization: i2pn2 (i2pn.org)
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On 5/9/24 11:38 AM, olcott wrote:
> On 5/8/2024 8:38 PM, immibis wrote:
>> On 8/05/24 21:05, olcott wrote:
>>> On 5/8/2024 10:13 AM, Mike Terry wrote:
>>>> On 08/05/2024 14:01, olcott wrote:
>>>>> 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)())
>>>>
>>>> HH is completely broken - it uses a global variable which is allows 
>>>> HH to detect whether it is the outer HH or a nested (simulated) HH. 
>>>> As a result, the nested HH behaves completely differently to the 
>>>> outer HH - I mean /completely/ differently: it goes through a 
>>>> totally separate "I am called in nested mode" code path!
>>>>
>>>
>>> The encoding of HH is not the pure function that it needs to be to
>>> be a computable function.
>>>
>>> *Maybe you can settle this*
>>>
>>> The disagreement is entirely over an enormously much simpler thing.
>>> The disagreement is that Richard says that a D simulated by H could
>>> reach past its own line 03 and halt.
>>
>> Here's the proof:
>>
>> 1. A simulation always produces an identical execution trace to the 
>> direct execution.
> 
> *When pathological self-reference is involved this is counter-factual*
> That no one can possibly show the steps of how D simulated by H possibly
> reach line 06 of H proves this.



> 
> Richard tried to get away with D never simulated by H as an example
> of D simulated by H:

Nope, you are looking at the WRONG message, and I have told you this 
multiple times.

Thus, you are proven to be just a stupid liar.

> 
> Message-ID: <v0ummt$2qov3$2@i2pn2.org>
> On 5/1/2024 7:28 PM, Richard Damon wrote:
> 
> *That people say they know I am wrong yet will not show the detailed*
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