XPost: comp.theory, sci.logic, sci.math
On 2/28/2022 1:49 PM,
dklei...@gmail.com wrote:
On Monday, February 28, 2022 at 7:58:51 AM UTC-8, olcott wrote:
PEOPLE AGREE WITH THIS
(1) It is the case that the simulated input ⟨Ĥ⟩ ⟨Ĥ⟩ to the copy of the
Linz H at Ĥ.qx (where H is a simulating halt decider) would have to
abort its simulation to prevent infinite simulation.
I don't.
The copy of H is a halting Turing Machine so cannot go infinite.
If the copy of H at Ĥ.qx never aborted its simulation then:
When Ĥ is applied to ⟨Ĥ⟩
Ĥ copies its input ⟨Ĥ1⟩ to ⟨Ĥ2⟩ then embedded_H simulates ⟨Ĥ1⟩ ⟨Ĥ2⟩
Then these steps would keep repeating:
Ĥ1 copies its input ⟨Ĥ2⟩ to ⟨Ĥ3⟩ then embedded_H simulates ⟨Ĥ2⟩ ⟨Ĥ3⟩
Ĥ2 copies its input ⟨Ĥ3⟩ to ⟨Ĥ4⟩ then embedded_H simulates ⟨Ĥ3⟩ ⟨Ĥ4⟩
Ĥ3 copies its input ⟨Ĥ4⟩ to ⟨Ĥ5⟩ then embedded_H simulates ⟨Ĥ4⟩ ⟨Ĥ5⟩...
Maybe you could get up to speed if you read my short paper:
https://www.researchgate.net/publication/358009319_Halting_problem_undecidability_and_infinitely_nested_simulation_V3
--
Copyright 2021 Pete Olcott
Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer
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