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

    It is not the case that Constructing a truth table requires explicit enumeration of 2^n rows, while a P=NP SAT algorithm need not enumerate valuations, making 'no harder than' equivocate on distinct complexity notions.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Both truth tables and P=NP SAT algorithms ultimately depend on evaluating formulas under valuations; the underlying hardness is identical.
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    • 2.Any algorithm deciding SAT on n variables must implicitly distinguish between 2^n cases; avoiding explicit enumeration doesn't eliminate the work.
      ?

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    • 3.Complexity theory measures computational operations, not data representation; whether output is 'enumerated' or 'implicit' is philosophically distinct from algorithmic hardness.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Truth tables require worst-case 2^n explicit row construction; P=NP SAT solvers could use shortcuts like unit propagation, avoiding full enumeration.
      ?

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    • 2.Worst-case and average-case complexity differ fundamentally; 'no harder than' conflates explicit construction time with decision time.
      ?

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    • 3.A polynomial SAT algorithm wouldn't need to output all valuations, only verify satisfiability, reducing information-theoretic requirements.
      ?

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