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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: =?UTF-8?Q?Re=3A_A_simulating_halt_decider_applied_to_the_The_Peter_?=
 =?UTF-8?Q?Linz_Turing_Machine_description_=E2=9F=A8=C4=A4=E2=9F=A9?=
Date: Mon, 27 May 2024 17:32:47 -0500
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On 5/27/2024 4:21 PM, Richard Damon wrote:
> On 5/27/24 3:45 PM, olcott wrote:
>> On 5/27/2024 11:33 AM, Richard Damon wrote:
>>> On 5/27/24 12:22 PM, olcott wrote:
>>>> On 5/27/2024 10:58 AM, Richard Damon wrote:
>>>>> On 5/27/24 11:46 AM, olcott wrote:
>>>>>> On 5/27/2024 10:25 AM, Richard Damon wrote:
>>>>>>> On 5/27/24 11:06 AM, olcott wrote:
>>>>>>
>>>>>>
>>>>>> typedef int (*ptr)();  // ptr is pointer to int function in C
>>>>>> 00       int H(ptr p, ptr i);
>>>>>> 01       int D(ptr p)
>>>>>> 02       {
>>>>>> 03         int Halt_Status = H(p, p);
>>>>>> 04         if (Halt_Status)
>>>>>> 05           HERE: goto HERE;
>>>>>> 06         return Halt_Status;
>>>>>> 07       }
>>>>>> 08
>>>>>> 09       int main()
>>>>>> 10       {
>>>>>> 11         H(D,D);
>>>>>> 12         return 0;
>>>>>> 13       }
>>>>>>
>>>>>> The above template refers to an infinite set of H/D pairs where D is
>>>>>> correctly simulated by either pure simulator H or pure function H. 
>>>>>> This
>>>>>> was done because many reviewers used the shell game ploy to endlessly
>>>>>> switch which H/D pair was being referred to.
>>>>>>
>>>>>> *Correct Simulation Defined*
>>>>>>     This is provided because many reviewers had a different notion of
>>>>>>     correct simulation that diverges from this notion.
>>>>>>
>>>>>>     A simulator is an x86 emulator that correctly emulates 1 to N 
>>>>>> of the
>>>>>>     x86 instructions of D in the order specified by the x86 
>>>>>> instructions
>>>>>>     of D. This may include M recursive emulations of H emulating 
>>>>>> itself
>>>>>>     emulating D.
>>>>>
>>>>> And how do you apply that to a TEMPLATE that doesn't define what a 
>>>>> call H means (as it could be any of the infinite set of Hs that you 
>>>>> can instantiate the template on)?
>>>>>
>>>>
>>>> *Somehow we got off track of the subject of this thread*
>>>
>>> I note that YOU keep on switching between your C program and Turing 
>>> Machines.
>>>
>>> Note, per the implications that you implicitly agreed to (by not even 
>>> trying to refute) the two systems are NOT equivalents of each other.
>>>
>>
>> (1) I think you are wrong. I have not seen any of your
>> reasoning that was not anchored in false assumptions.
>> Your make fake rebuttal is to change the subject.
>>
>> (2) It does not matter my proof is anchored in the Linz
>> proof and the H/D pairs are only used to have a 100% concrete
>> basis to perfectly anchor things such as the correct meaning
>> of D correctly simulated by H so that people cannot get away
>> with claiming that an incorrect simulation is correct.
>>
>> int main() { D(D); } IS NOT THE BEHAVIOR OF D CORRECTLY SIMULATED BY H.
>> One cannot simply ignore the pathological relationship between H and D.
>>
>>>>
>>>> When Ĥ is applied to ⟨Ĥ⟩
>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>
>>>>   Ĥ copies its own Turing machine description: ⟨Ĥ⟩
>>>>   then invokes embedded_H that simulates ⟨Ĥ⟩ with ⟨Ĥ⟩ as input.
>>>>
>>>> For the purposes of the above analysis we hypothesize that
>>>> embedded_H is either a UTM or a UTM that has been adapted
>>>> to stop simulating after a finite number of steps of simulation.
>>>
>>> And what you do mean by that?
>>>
>>> Do you hypothesize that the original H was just a pure UTM,
>>
>> The original proof does not consider the notion of a simulating
>> halt decider so I have to begin the proof at an earlier stage
>> than any definition of H.
> 
> The biggest problem is that the input to the Turing machine decider H is 
> the description of a Turing Machine H^, which is a SPECIFIC machine, 

When you say "specific machine" you don't mean anything like a
100% completely specified sequence of state transitions encoded
as a single unique finite string.



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