• Concise refutation of halting problem proofs V47

    From olcott@21:1/5 to All on Sat Jan 8 19:41:26 2022
    XPost: comp.theory, sci.logic, sci.math

    // Simplified Linz(1990) Ĥ
    // and Strachey(1965) P
    void P(ptr x)
    {
    if (H(x, y))
    HERE: goto HERE;
    }

    H and P are defined according to the standard HP counter-example
    template shown above.

    H bases its halt status decision on the behavior of the simulation of
    its input.

    Then P demonstrates an infinitely repeating pattern that cannot possibly
    ever reach its final state.

    This conclusively proves that the input to H meets the Linz definition
    of non-halting:

    computation that halts … the Turing machine will halt whenever it enters
    a final state. (Linz:1990:234)

    thus the sufficiency condition for H to report that its input specifies
    a non-halting computation.

    Halting problem undecidability and infinitely nested simulation V2 https://www.researchgate.net/publication/356105750_Halting_problem_undecidability_and_infinitely_nested_simulation_V2


    --
    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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