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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that Diagonalization cannot be used to separate P from NP.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Non-relativizing proof techniques (e.g., arithmetization used in IP=PSPACE) demonstrate that oracle barriers do not constrain all possible proof strategies.
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    • 2.The Baker-Gill-Solovay result shows diagonalization-based proofs cannot resolve P vs NP, not that diagonalization itself is categorically excluded as a component of a hybrid proof.
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    • 3.A proof incorporating diagonalization alongside non-relativizing elements would not be subject to the relativization barrier, leaving the claim's scope critically under-specified.
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    Reason for 2 of 2
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    • 1.The relativization barrier is a property of proof methods, not of mathematical facts, so oracle separation results constrain epistemology, not the underlying separation itself.
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    • 2.Razborov and Rudich's natural proofs barrier and Aaronson and Wigderson's algebrization barrier each identify distinct obstacles, implying no single barrier argument is sufficient to foreclose all diagonalization variants.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Baker, Gill, and Solovay (1975) established oracles A and B such that P^A = NP^A and P^B ≠ NP^B.
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    • 2.A proof of P ≠ NP based on diagonalization would relativize to both oracle A and oracle B.
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    • 3.A method that relativizes to both A and B cannot separate P and NP, since P^A = NP^A.
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