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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 11:22:03 -0500
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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*

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.

 From this we can see that ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H
cannot possibly reach its own simulated final state of ⟨Ĥ.qn⟩ and halt
in an infinite or any finite sequence of correctly simulated steps.

When an infinite number of steps is not enough then we can definitely
conclude that less than an infinite numbers of steps is also not enough.



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