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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: D correctly simulated by H cannot possibly halt --- templates and
 infinite sets --- deciders
Date: Thu, 30 May 2024 21:37:30 -0400
Organization: i2pn2 (i2pn.org)
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On 5/30/24 10:43 AM, olcott wrote:
> On 5/28/2024 11:16 AM, olcott wrote:
>>
>> When Ĥ is applied to ⟨Ĥ⟩
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>
>> *Formalizing the Linz Proof structure*
>> ∃H  ∈ Turing_Machines
>> ∀x  ∈ Turing_Machines_Descriptions
>> ∀y  ∈ Finite_Strings
>> such that H(x,y) = Halts(x,y)
>>
> 
> A decider computes the mapping from finite string inputs to
> its own accept or reject state.

Right, and to be a "foo" decider, that mapping must map the "foo" 
mapping, so a Halt Decider must compute the "Halts" funciton, which is 
True if teh Turing Machine described by the input halts o the other 
input given.

> 
> A decider does not and cannot compute the mapping from
> Turing_Machine inputs to its own accept or reject state.

But it can from the representation of said Turing Machine, which is a 
finite string.

> 
> Halts(x,y) would report on the direct execution of x(y) thus ignores
> the pathological behavior of x correctly simulated by pure function H.
> This makes Halts(x,y) an incorrect measure of the correctness of H(x,y).

And, if that keeps H from being able to answer, that makes Halts 
uncomputable, and thus there are no such things as correct Halt Deciders.

And you have it backwards, Halts *IS* BY DEFINITION, the DEFINITION of 
what H needs to produce if it is to be a *HALT* decider.

You are just showing your ignorance of the meaning of the words.

> 
> This is easier to see when we can see every single detail of all of
> the steps as an x86 execution trace of D correctly simulated by pure
> function H.
> 
> typedef int (*ptr)();  // ptr is pointer to int function in C
> 00       int HH(ptr p, ptr i);
> 01       int DD(ptr p)
> 02       {
> 03         int Halt_Status = HH(p, p);
> 04         if (Halt_Status)
> 05           HERE: goto HERE;
> 06         return Halt_Status;
> 07       }
> 08
> 09       int main()
> 10       {
> 11         HH(DD,DD);
> 12         return 0;
> 13       }
> 
> *Begin simulation of DD by HH*
> Begin Local Halt Decider Simulation   Execution Trace Stored at:113075
> [00001c22][00113061][00113065] 55         push ebp
> [00001c23][00113061][00113065] 8bec       mov ebp,esp
> [00001c25][0011305d][00103031] 51         push ecx
> [00001c26][0011305d][00103031] 8b4508     mov eax,[ebp+08]
> [00001c29][00113059][00001c22] 50         push eax         ; push DD
> [00001c2a][00113059][00001c22] 8b4d08     mov ecx,[ebp+08]
> [00001c2d][00113055][00001c22] 51         push ecx         ; push DD
> [00001c2e][00113051][00001c33] e80ff7ffff call 00001342    ; call HH
> New slave_stack at:14da95

WRONG!!!
the CORRECT simulation needs to show the actual INSTRUCTIONS of HHJ.
YOu are just showing that you don't understand the meaning of the words 
you are using

> [00001c22][0015da89][0015da8d] 55         push ebp
> [00001c23][0015da89][0015da8d] 8bec       mov ebp,esp
> [00001c25][0015da85][0014da59] 51         push ecx
> [00001c26][0015da85][0014da59] 8b4508     mov eax,[ebp+08]
> [00001c29][0015da81][00001c22] 50         push eax         ; push DD
> [00001c2a][0015da81][00001c22] 8b4d08     mov ecx,[ebp+08]
> [00001c2d][0015da7d][00001c22] 51         push ecx         ; push DD
> [00001c2e][0015da79][00001c33] e80ff7ffff call 00001342    ; call HH
> Local Halt Decider: Recursive Simulation Detected Simulation Stopped
> 
> DD correctly simulated by HH cannot possibly reach its own simulated
> final state at line 06 in any number of steps including an infinite
> number of steps because DD correctly simulated by HH remains stuck in
> recursive simulation.
> 

But that isn't the question for a HALT decicer.

Maybe for a POOP decider, but who cares about that, and you keep on 
LYING about H being a Halt Decider, and then reject the actual definiton 
of a Halt Decider.