• Concise refutation of halting problem proofs V28 [ finally mathematical

    From olcott@21:1/5 to All on Mon Nov 22 15:16:05 2021
    XPost: comp.theory, sci.logic, sci.math

    #include <stdint.h>
    #include <stdio.h>
    typedef int (*ptr)();

    int H(ptr x, ptr y)
    {
    x(y); // direct execution of P(P)
    return 1;
    }

    // Minimal essence of Linz(1990) Ĥ
    // and Strachey(1965) P
    int P(ptr x)
    {
    H(x, x);
    return 1; // Give P a last instruction at the "c" level
    }

    int main(void)
    {
    H(P, P);
    }

    Computation that halts
    a computation is said to halt whenever it enters a final state.
    (Linz:1990:234)

    [PSR_set] Combinations of H/P having pathological self-reference
    For every H of H(P,P) where P(P) calls this same H(P,P) and H simulates
    or executes its input and aborts or does not abort its input.

    [PSR_set] ∀{H,P} ∊ PSR_set (Input_Never_Halts( H(P,P) ))
    [PSR_subset_A] ∃{H,P} ∊ PSR_set (Halts( H(P,P) ))
    [PSR_subset_B] ∃{H,P} ∊ PSR_set (Halts( P(P) ))

    [PSR_subset_C] The subset of the PSR_subset_A where H returns 0 on the
    basis that H correctly detects that its input never halts (reaches its
    final instruction). H could detect that its simulated P is calling
    H(P,P) with the same parameters that it was called with, thus specifying infinite recursion.

    H is a computable function that accepts or rejects inputs in its domain
    on the basis that these inputs specify a sequence of configurations that
    reach their final state.
    H is a correct decider and H has a correct halt deciding basis.

    *(see page 3)*
    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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