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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that Immerman and Vardi's theorem requires that order be present in the structure, so the logical reformulation captures only a restricted variant of P vs NP, not the general problem as standardly posed.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Ordering can be added as auxiliary structure without changing computational complexity; P vs NP equivalence holds across these representations.
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    • 2.Immerman-Vardi captures the essential logical content of P: solvability by deterministic polynomial-time algorithms, regardless of structural encoding.
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    • 3.No standard P vs NP instance avoids structure entirely; graphs, formulas, and numbers inherently carry relational information comparable to ordering.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Immerman-Vardi requires ordered structures; unordered structures lack built-in successor relations needed for their fixed-point characterizations.
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    • 2.Standard P vs NP makes no ordering assumption; solutions should work on any finite structure, not just ordered ones.
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    • 3.Restricting to ordered structures may exclude hard instances; expressive power could differ meaningfully between ordered and unordered settings.
      ?

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