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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that P equals coP

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.The closure of P under complementation establishes coP ⊆ P, but does not establish that every problem in coP has a polynomial-time algorithm for its positive instances.
      ?

      Think about whether this reason is strong or weak

    • 2.Conflating syntactic closure properties with semantic decidability equivocates between computational and logical notions of symmetry, a distinction central to complexity-theoretic separations.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.The oracle separation results of Baker, Gill, and Solovay (1975) demonstrate that P=coP holds relative to some oracles and fails relative to others, undermining any purely structural proof.
      ?

      Think about whether this reason is strong or weak

    • 2.If the equality P=coP were trivially entailed by closure properties alone, it would collapse the polynomial hierarchy in ways inconsistent with widely accepted complexity-theoretic conjectures such as PH being infinite.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.P is closed under complementation
      ?

      Think about whether this reason is strong or weak

    • 2.coC is defined as the class of problems whose complements are in class C
      ?

      Think about whether this reason is strong or weak

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