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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that A proof of P ≠ NP is beyond the reach of currently known proof techniques.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Razborov and Rudich's natural proofs barrier presupposes strong pseudorandom function assumptions; if one-way functions do not exist, the barrier dissolves.
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    • 2.The claim that proof techniques are insufficient conflates contingent cryptographic assumptions with necessary logical limitations on mathematical method.
      ?

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    • 3.A proof technique blocked under one set of background assumptions may become viable if those assumptions are revised, so the barrier is conditional, not absolute.
      ?

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    Reason for 2 of 2
    ?
    • 1.The relativization barrier (Baker-Gill-Solovay) shows diagonalization fails, but non-relativizing techniques like arithmetization already exist and succeeded in proving IP=PSPACE.
      ?

      Think about whether this reason is strong or weak

    • 2.The existence of at least one successful non-relativizing proof method refutes the inductive generalization that no currently known technique can yield complexity separations.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Known proof methods such as diagonalization relativize and therefore cannot separate P from NP.
      ?

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    • 2.Approaches such as geometric complexity theory are still in need of substantial refinement.
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    • 3.No currently known method is sufficient to yield the desired separation between P and NP.
      ?

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    Strongest counterpoint
    Explore the most compelling reason on the other side.