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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: =?UTF-8?Q?Re=3A_A_simulating_halt_decider_applied_to_the_The_Peter_?=
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Date: Sun, 26 May 2024 21:43:11 -0500
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On 5/26/2024 9:06 PM, 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
> 
>   Ĥ copies its own Turing machine description: ⟨Ĥ⟩
>   then invokes embedded_H that simulates ⟨Ĥ⟩ with ⟨Ĥ⟩ as input.
> 
> It is an easily verified fact that ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by
> embedded_H cannot possibly reach its own simulated final state of
> ⟨Ĥ.qn⟩ in any finite sequence of steps.

*To other reviewers that are not dishonest*
The complete proof of the above statement is that when we hypothesize
that embedded_H is a UTM we can see that:

⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by UTM embedded_H cannot possibly reach its
own simulated final state of ⟨Ĥ.qn⟩ in an infinite number of steps.

This conclusively proves that ⟨Ĥ⟩ will not reach ⟨Ĥ.qn⟩ is less than
an infinite number of steps. A decider is not allowed to simulate
an infinite number of steps.



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