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

Op 30.mei.2024 om 19:00 schreef olcott:

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.
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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.

Incorrect. Your own words are that lines 04, 05 and 06 are nor reachable for the simulator. The simulator does not even simulate that part of D, so that cannot be the reason. If lines 04, 05 and 06 are removed, then the simulation of H will still not reach its final state.
It is completely illogical to claim that the reason that line 04 cannot be reached is the behaviour of line 05 and 06.
Do you understand C? If line 04 cannot be reached, lines 05 and 06 do not cause any behaviour.

 

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.
 

It is H that keeps repeating the simulation of D and the next H, so the simulated H never reaches its abort, so it does not reach its final state. D acts only as a quick parameter duplicator so that H simulates itself. Then H gets stuck in an infinite recursion and never reaches the 'pathological' part of D. Even a beginner will see that if the simulated H would really halt, then D would continue to line 04.