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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: Thu, 9 May 2024 20:07:04 -0500
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On 5/9/2024 6:43 PM, Mike Terry wrote:
> On 09/05/2024 04:46, olcott wrote:
>> On 5/8/2024 10:05 PM, Mike Terry wrote:
>>> On 08/05/2024 20:05, 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.
>>>>
>>>
>>> I'll respond with my assessment on this, provided you agree in 
>>> advance that you won't quote me elsewhere [in other threads/forums] 
>>> in support of your claims.  Not that I can really enforce 
> 
> ..NOTE: not in other THREADS or forums, i.e. NOT in other threads on 
> these newsgroups.  (Just in this specific thread, where what I say will 
> be quoted automatically by your newsreader!  I can't see why you would 
> quote me in other threads anyway other than in some kind of attempt to 
> shut down discussion in your favour...)
> 
>>> this, but I think for the most part you are basically honest, and 
>>> would try to keep an agreement you made on this, if you chose to make 
>>> one.
>>>
>>
>> That is really great Mike, you have been a wonderful help.
>> I will agree not to quote you anywhere else but these two
>> forums and I am nearly certain that I never quoted anyone
>> else from these forums anywhere else besides these forums.
>>
>>> You understand the reason I ask this:  you are unfortunately 
>>> completely unable to judge what other people say to you, and as soon 
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