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

On 5/30/2024 10:20 AM, Fred. Zwarts wrote:

Op 30.mei.2024 om 16:43 schreef olcott:

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

 Why are you referring to the 'pathological behavior of x' if your claim is that the simulator does not even reach the part of DD (below) that contradicts the result of HH? This 'pathological behavior of x' is completely irrelevant.

The actual behavior of DD correctly simulated by ANY pure function H
is that DD never reaches its own simulated final state at line 06 and
halts and pure function H halts.
You are simply not paying close enough attention to the exact meaning of
my words.

The problem is that a simulating decider is unable to handle the simulation of itself because it gets stuck in recursive simulation). That DD contradicts HH's result is completely irrelevant.
 

>
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       }

 

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