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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
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    Inverse View

    It is not the case that 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.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Oracle results show which proof techniques fail, not that structural proofs are impossible—natural models may still permit structural arguments unavailable relativistically.
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    • 2.The claim conflates 'relativizing proofs don't work' with 'structural proofs don't work,' but non-relativizing structural arguments could still exist and succeed.
      ?

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    • 3.BGS demonstrates limitations of one proof paradigm, not that all structural reasoning about complexity classes is futile or fundamentally undermined by oracles.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Oracle separations reveal that proof techniques depending only on abstract structural properties cannot settle P vs coP, limiting purely axiomatic approaches.
      ?

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    • 2.The existence of oracles where P≠coP shows these complexity classes are fundamentally different in some models, suggesting structural arguments alone are insufficient.
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    • 3.BGS results establish that any resolution of P=coP must use non-relativizing techniques exploiting concrete computational properties, not generic reasoning.
      ?

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