• General Undecidable Axiom(2021 WIJ)

    From wij@21:1/5 to All on Sat Jul 10 18:54:41 2021
    Since the conventional HP only mentions a specific halting problem, which is often believed to be an invalid proof.
    See https://groups.google.com/g/comp.theory/c/RO9Z9eCabeE/m/Ka8-xS2rdEEJ

    I hereby claims the General Undecidable Axiom(2021 WIJ): +--------------------------------------------------------------------------------+
    | No TM U can decide the property of a TM P if that property can be defied by TM P. |
    +--------------------------------------------------------------------------------+

    // Example1:
    // [Ret] true: f prints 'Y'
    // false: f does not print 'Y'
    bool U(Func f);

    void P() {
    if(U(P)) {
    printf("b");
    } else {
    printf("Y");
    }
    }
    //---

    // Example2:
    // [Ret] true: f is a "pathological self-reference" function
    // false: otherwise
    bool U(Func f);

    void P() {
    if(U(P)) {
    return;
    } else {
    P(); // if "pathological self-reference" is so defined, whatever.
    }
    };

    ------------------------
    The construct of P (proof of General Undecidable Axiom) is 100% correct, intuitive and above all, REPRODUCIBLE, VERIFIABLE.

    // [Ret] true: f has the (dynamic)property Q
    // false: otherwise
    bool U(Func f);

    void P() {
    if(U(P)) {
    // do whatever Q defines false
    } else {
    // do whatever Q defines
    }
    };

    Note: I would like to acknowledge Olcott tirelessly refuted various conventional
    HP proofs over these years. So I need not to do the same work again, though not necessary.

    Copyright 2021 WIJ

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From wij@21:1/5 to wij on Sat Jul 31 04:12:21 2021
    On Sunday, 11 July 2021 at 09:54:43 UTC+8, wij wrote:
    Since the conventional HP only mentions a specific halting problem, which is often believed to be an invalid proof.
    See https://groups.google.com/g/comp.theory/c/RO9Z9eCabeE/m/Ka8-xS2rdEEJ

    I hereby claims the General Undecidable Axiom(2021 WIJ): +--------------------------------------------------------------------------------+
    | No TM U can decide the property of a TM P if that property can be defied by TM P. |
    +--------------------------------------------------------------------------------+

    // Example1:
    // [Ret] true: f prints 'Y'
    // false: f does not print 'Y'
    bool U(Func f);

    void P() {
    if(U(P)) {
    printf("b");
    } else {
    printf("Y");
    }
    }
    //---

    // Example2:
    // [Ret] true: f is a "pathological self-reference" function
    // false: otherwise
    bool U(Func f);

    void P() {
    if(U(P)) {
    return;
    } else {
    P(); // if "pathological self-reference" is so defined, whatever.
    }
    };

    ------------------------
    The construct of P (proof of General Undecidable Axiom) is 100% correct, intuitive and above all, REPRODUCIBLE, VERIFIABLE.

    // [Ret] true: f has the (dynamic)property Q
    // false: otherwise
    bool U(Func f);

    void P() {
    if(U(P)) {
    // do whatever Q defines false
    } else {
    // do whatever Q defines
    }
    };

    Note: I would like to acknowledge Olcott tirelessly refuted various conventional
    HP proofs over these years. So I need not to do the same work again, though not necessary.

    Copyright 2021 WIJ

    This was a joke. The copyright is removed (Public Domain) https://groups.google.com/g/comp.theory/c/_tbCYyMox9M

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)