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    Carmelics

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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 If P equals NP, finding a satisfying valuation for a propositional formula would be no harder than constructing its truth table

    ?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.Computational hardness is a property of problem classes under worst-case inputs, not a uniform measure of cognitive or procedural difficulty.
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    • 2.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.
      ?

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    • 3.Aaronson and others in computational complexity theory distinguish between polynomial-time equivalence and step-by-step procedural comparability, which the claim conflates.
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    Reason for 2 of 2
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    • 1.The claim presupposes a Platonist reading of complexity classes as describing intrinsic difficulty, whereas constructivists like Bridges and Richman argue complexity is relative to the formal system and proof methods available.
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      Think about whether this reason is strong or weak

    • 2.If P=NP were proven non-constructively, we might establish equivalence without possessing the actual efficient algorithm, leaving the epistemic gap between finding and constructing intact.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Constructing the truth table of a propositional formula is a polynomial-time task
      ?

      Think about whether this reason is strong or weak

    • 2.Finding a satisfying valuation for a propositional formula is an NP problem
      ?

      Think about whether this reason is strong or weak

    • 3.If P equals NP, the difficulty of finding and verifying solutions to all NP problems coincides
      ?

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    Strongest counterpoint
    Explore the most compelling reason on the other side.