Re: A simulating halt decider applied to the The Peter Linz Turing Machine description ⟨Ĥ⟩

On 5/26/2024 9:30 PM, Richard Damon wrote:

On 5/26/24 10:06 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 such as Googolplex ^ Googolplex
number of steps. https://en.wikipedia.org/wiki/Googolplex

 So, it can verify that if H / embedded_H was programmed not to halt it simulation, then the H^ built on that H will be non-halting, but that doesn't say anything about the DIFFERENT H^ built on an H that does abort its simulation and returns 0.
 

You really do have an actual problem paying attention.
It is not a mere trollish ruse. I poured engine oil
into my power steering fluid Friday night so I can relate.
As far as paying attention to words that have been written
I read and reread many times until I am sure that I get it.
Even then I get it wrong once in a while.
When embedded_H correctly simulates a Googolplex ^ Googolplex steps
of ⟨Ĥ⟩ ⟨Ĥ⟩ then embedded_H halts.
⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H cannot possibly reach its
own simulated final state of ⟨Ĥ.qn⟩ in any finite 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