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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 19:08:00 -0500
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On 5/27/2024 5:44 PM, Richard Damon wrote:
> On 5/27/24 6:32 PM, olcott wrote:
>> 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.
> 
> Mostly.
> 
> There doesn't need to be a unique finite string, but it is a 100% 
> completely specified state transition/tape operation table.
> 

When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

In other words Linz did not prove that there are no set
of state transitions specified by ⊢* that derives the
correct halt status of ⟨Ĥ⟩ ⟨Ĥ⟩.

He only said there there is one specific machine that
gets the wrong answer.


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