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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Two dozen people were simply wrong --- Try to prove otherwise
Date: Thu, 30 May 2024 08:31:29 -0500
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On 5/30/2024 2:40 AM, Mikko wrote:
> On 2024-05-30 01:15:21 +0000, olcott said:
> 
>> On 5/29/2024 8:07 PM, Richard Damon wrote:
>>> On 5/29/24 8:59 PM, olcott wrote:
>>>> On 5/29/2024 7:48 PM, Richard Damon wrote:
>>>>> On 5/29/24 8:17 PM, olcott wrote:
>>>>>> On 5/29/2024 7:09 PM, Richard Damon wrote:
>>>>>>> On 5/29/24 7:57 PM, olcott wrote:
>>>>>>>> On 5/29/2024 6:47 PM, Richard Damon wrote:
>>>>>>>>> On 5/29/24 2:31 PM, olcott wrote:
>>>>>>>>>> On 5/29/2024 1:14 PM, Ben Bacarisse wrote:
>>>>>>>>>>> Alan Mackenzie <acm@muc.de> writes:
>>>>>>>>>>>
>>>>>>>>>>>> How about a bit of respect?  Mike specifically asked you not 
>>>>>>>>>>>> to cite his
>>>>>>>>>>>> name as a back up for your points.  Why do you keep doing it?
>>>>>>>>>>>
>>>>>>>>>>> He does it to try to rope more people in.  It's the same ploy as
>>>>>>>>>>> insulting people by name.  It's hard to ignore being maligned 
>>>>>>>>>>> in public
>>>>>>>>>>> by a fool.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> *Thanks for validating my simplified encoding of the Linz*
>>>>>>>>>>
>>>>>>>>>> When Ĥ is applied to ⟨Ĥ⟩
>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>
>>>>>>>>>> I really did believe that Ben Bacarisse was lying when I said it.
>>>>>>>>>>
>>>>>>>>>> At the time I was talking about the easily verified fact of 
>>>>>>>>>> the actual
>>>>>>>>>> execution trace of fully operational code and everyone was 
>>>>>>>>>> denying the
>>>>>>>>>> easily verified facts.
>>>>>>>>>>
>>>>>>>>>> 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       }
>>>>>>>>>>
>>>>>>>>>> It turns out that two dozen people are easily proven wrong when
>>>>>>>>>> they claimed that the correct simulation of the input to H(D,D)
>>>>>>>>>> is the behavior of int main() { D(D); }
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> How is that?
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>> When D is correctly simulated by H using an x86 emulator the only
>>>>>>>>>> way that the emulated D can reach its own emulated final state
>>>>>>>>>> at line 06 and halt is
>>>>>>>>>> (a) The x86 machine code of D is emulated incorrectly
>>>>>>>>>> (b) The x86 machine code of D is emulated in the wrong order
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Which isn't a "Correct Simulation" by the definition that allow 
>>>>>>>>> the relating of a "Simulation" to the behavior of an input.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Right the execution trace of D simulated by pure function H using
>>>>>>>> an x86 emulator must show that D cannot possibly reach its own
>>>>>>>> simulated final state and halt or the simulation of the machine
>>>>>>>> language of D is incorrect or in the wrong order.
>>>>>>>
>>>>>>> So, you aren't going to resolve the question but just keep up 
>>>>>>> with your contradiction that H is simulating a template (that 
>>>>>>> doesn't HAVE any instrucitons of H in it) but also DOES simulate 
>>>>>>> those non-existance instructions by LYING about what it does and 
>>>>>>> simulating a SPECIFIC instance that it LIES behaves just like 
>>>>>>> DIFFERENT specific instatces.
>>>>>>
>>>>>> I will give you the benefit of the doubt and call that an honest
>>>>>> misunderstanding. I have much more empathy for you now that I found
>>>>>> that Linz really did say words that you could construe as you did.
>>>>>>
>>>>>> The infinite set of every H/D pair specified by the template
>>>>>> where D is correctly simulated by pure simulator H or pure function
>>>>>> H never has any D reach its own simulated final state and halt.
>>>>>
>>>>> But the question ISN'T about the SIMULATED D, but about the 
>>>>> behavior of the actual PROGRAM/MACHINE D
>>>>>
>>>>> This seems to be your blind spot.
>>>>
>>>> ∃H  ∈ Turing_Machines
>>>> ∀x  ∈ Turing_Machines_Descriptions
>>>> ∀y  ∈ Finite_Strings
>>>> such that H(x,y) = Halts(x,y)
>>>>
>>>> Not really the above formalization does not can cannot
>>>> specify Turing Machines as the input to any decider H.
>>>>
>>>
>>> Then what is x representing?
>>
>> x <is> a finite string Turing machine description that SPECIFIES 
>> behavior. The term: "representing" is inaccurate.
> 
> No, x is a description of the Turing machine that specifies the behaviour
> that H is required to report. 

That is what I said.

> The maning of x is that there is a universal
> Turing machine that, when given x and y, simulates what the described
> Turing machine does when given y. 

Yes that is also correct.

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

When embedded_H is a UTM then it never halts.

When embedded_H is a simulating halt decider then its correctly
simulated input never reaches its own simulated final state of
⟨Ĥ.qn⟩ and halts. H itself does halt and correctly rejects its
input as non-halting.


> Therefore, you may reformulate the
> requirement:
> 
> ∀x  ∈ Turing_Machines_Descriptions
> ∀y  ∈ Finite_Strings
> H(x,y) returns "yes" if UTM(x,y) halts and "no" otherwise.
> 

Not quite.

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