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computers / comp.ai.philosophy / What final state does adapted Linz Ĥ applied to ⟨Ĥ⟩ transition to? [no loop]

What final state does adapted Linz Ĥ applied to ⟨Ĥ⟩ transition to? [no loop]

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From: NoO...@NoWhere.com (olcott)
Subject: What_final_state_does_adapted_Linz_Ĥ_applied_to_
⟨Ĥ⟩ transition to? [no loop]
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by: olcott - Fri, 24 Dec 2021 20:37 UTC

The following is the exact Linz Ĥ applied to its own Turing machine
description except that the infinite loop appended to the YES path has
been removed.

Ḧq0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qy
Ḧq0 ⟨Ḧ⟩ ⊢* Ḧ.qx ⟨Ḧ⟩ ⟨Ḧ⟩ ⊢* Ḧ.qn

The copy of H at Ḧ.qx maps ⟨Ḧ⟩ ⟨Ḧ⟩ to a final state on the basis of the
behavior of the pure simulation of N steps of ⟨Ḧ⟩ applied to ⟨Ḧ⟩

It performs a pure simulation of its input until:
(a) Its input halts on its own, then it transitions to Ḧ.qy.

(b) It determines that the pure simulation of its input would never halt
on its own, then it aborts its simulation and transitions to Ḧ.qn.

https://www.liarparadox.org/Peter_Linz_HP_315-320.pdf
Linz, Peter 1990. An Introduction to Formal Languages and Automata.
Lexington/Toronto: D. C. Heath and Company. (315-320)

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

Subject	Author
What final state does adapted Linz Ĥ applied to	olcott