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.

It is totally relevant because it is the reason why D correctly
simulated by H cannot possibly halt.

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.
 

The simulating decider does not get stuck in recursive simulation
it detects the repeating state of D and stops simulating.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer