Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets --- deciders

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.