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From: Richard Damon <richard@damon-family.org>
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 18:44:34 -0400
Organization: i2pn2 (i2pn.org)
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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.

Note, the sequences of states it goes through, will be a function of the 
input given to that machine.

No no-trival Turing machine has a unique finite string encoding because 
you can always re"name" the non-initial/non-final states generating a 
vast array of possible encodings (generally an infinite number of them)

Does that surprise you? It shouldn't

Note, that specific Turing machine H^ needs to be built from the 
specific Turing Machine H that it is being built to refute as being correct.

The key is we can show that for ANY machine that might claim to be a 
correct halt decider, the proof establishes a formula to construct a 
specific input you can give that specific machine to show that it isn't 
correct.