• Concise refutation of halting problem proofs V55 [ halt deciders ]

    From olcott@21:1/5 to All on Fri Jan 28 19:14:26 2022
    XPost: comp.theory, sci.logic, sci.math

    Because halt deciders are deciders they are only accountable for
    computing the mapping their actual input finite strings to an accept or
    reject state on the basis of the actual behavior specified by these
    actual inputs.

    It is like you put a guard on the front door that is supposed to report
    anyone coming in the front door (the actual inputs). Then someone comes
    in the back door (non inputs) and the guard does not report this.

    Since the guard is only supposed to report people coming in the front
    door (actual inputs) it is incorrect to say that the guard made a
    mistake by not reporting people that came in the back door (non inputs).

    Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
    Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

    The copy of Linz H at Ĥ.qx (embedded_H) determines the halt status of
    its input on the basis of whether or not the pure simulation of any
    finite number of steps of this input can possibly ever reach a final
    state of this simulated input.

    When embedded_H correctly determines that its simulated input would
    never reach its final state it aborts its input and transitions to Ĥ.qn.

    When this causes Ĥ applied to ⟨Ĥ⟩ to halt that makes no difference because the guard is only accountable for watching the front door.

    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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