• Proving that H(P,P)==0 on the basis of easily verified facts (tiny typo

    From olcott@21:1/5 to All on Wed Jun 15 17:44:47 2022
    XPost: comp.theory, sci.logic, sci.math

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

    void P(ptr x)
    {
    if (H(x, x))
    HERE: goto HERE;
    return;
    }

    int main()
    {
    Output("Input_Halts = ", H(P, P));
    }

    _P()
    [00001352](01) 55 push ebp
    [00001353](02) 8bec mov ebp,esp
    [00001355](03) 8b4508 mov eax,[ebp+08]
    [00001358](01) 50 push eax // push P
    [00001359](03) 8b4d08 mov ecx,[ebp+08]
    [0000135c](01) 51 push ecx // push P
    [0000135d](05) e840feffff call 000011a2 // call H
    [00001362](03) 83c408 add esp,+08
    [00001365](02) 85c0 test eax,eax
    [00001367](02) 7402 jz 0000136b
    [00001369](02) ebfe jmp 00001369
    [0000136b](01) 5d pop ebp
    [0000136c](01) c3 ret
    Size in bytes:(0027) [0000136c]

    (1) It is an easily verified fact that when we assume that H is only an
    x86 emulator that the correctly emulated P never reaches its "ret"
    instruction.

    (2) It is an easily verified fact that if H has been adapted to
    correctly detect (in a finite number of steps) that the correct and
    complete x86 emulation of its input would never each its "ret"
    instruction that H could abort its emulation and return 0 to report this.

    (3) When the halt status criteria is defined as correctly determining
    whether or not an x86 emulated input would ever reach its "ret"
    instruction then it becomes an easily verified fact H(P,P) could
    correctly reject its input as non-halting.

    Correct deductive inference proves that all of these things are true
    without any need what-so-ever to see either the source-code or the
    execution trace of H.

    The one thing that is not proved is whether or not an actual encoded
    H(P,P) does indeed correctly determine that its input would never reach
    its "ret" instruction as a pure function of its inputs.


    Halting problem undecidability and infinitely nested simulation (V5)

    https://www.researchgate.net/publication/359984584_Halting_problem_undecidability_and_infinitely_nested_simulation_V5


    --
    Copyright 2022 Pete Olcott

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

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