• =?UTF-8?Q?=E2=84=99=E2=89=A0=E2=84=95=E2=84=99?= proof

    From wij@3:633/280.2 to All on Sun Feb 4 14:11:23 2024
    This file is intended a proof that =E2=84=99=E2=89=A0=E2=84=95=E2=84=99.=
    =20 https://sourceforge.net/projects/cscall/files/MisFiles/PNP-proof.txt/downlo=
    ad

    -------------
    ANPC::=3D Set of decision problems that additional information c must be provided
    to compute the problem in P-time (including processing the
    information c
    (certificate)).

    Since the information c can be generated in O(2^N) time, the upper
    bound of
    ANPC is O(2^N) (checking c is in P-time).

    Corollary: ANPC =E2=8A=86 =E2=84=95=E2=84=99 (from =E2=84=95=E2=84=99 defin= ition: "... =E2=84=95=E2=84=99 is the set of
    decision
    problems verifiable in polynomial time by a deterministic Turing
    machine. https://en.wikipedia.org/wiki/NP_(complexity)")

    If we try to prove or show that an ANPC problem can be solved in P-
    time, we=20
    would also be trying to prove/show that the requirement of the
    additional=20
    information c is not necessary. Thus, such a proof will just prove
    itself not a valid proof, IOW, ANPC=3D=3DP is unprovable.

    Conclusion: ANPC is not P-time provable/solvable (implied by ANPC
    definition)

    Corollary: =E2=84=95=E2=84=99!=3D=E2=84=99 (ANPC =E2=8A=86 =E2=84=95=E2=84=
    =99 AND ANPC!=3D=E2=84=99)

    QED. ------------=20




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