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    Made withinDC&Austin
    Home/Original/inverse
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    Inverse View

    It is not the case that Diagonalization cannot be used to separate P and 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.Relativization barriers show only that *relativizing* diagonalization fails, not that all diagonalization-based techniques are exhausted.
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    • 2.Non-relativizing proof techniques (e.g., arithmetization underlying IP=PSPACE) demonstrate that diagonal-style separation methods can escape oracle limitations.
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    • 3.Therefore the BGS result eliminates a proof *strategy*, not the broader family of diagonalization-inspired arguments that exploit circuit lower bounds or non-uniform complexity.
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    Reason for 2 of 2
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    • 1.The BGS oracle argument presupposes that a valid P≠NP proof must be syntactically relativizable, but this is a methodological assumption, not a logical necessity.
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    • 2.Razborov and Rudich's 'natural proofs' barrier is a distinct obstruction, confirming that relativization alone does not fully characterize the space of impossible proof strategies.
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    • 3.Claiming diagonalization *cannot* separate P and NP conflates one well-defined barrier (relativization) with an exhaustive prohibition, thereby overstating what BGS actually proved.
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    Reasons Against

    1 perspective
    Reason against
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    • 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.No single diagonalization argument can simultaneously yield P^A = NP^A and P^B ≠ NP^B
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