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    Carmelics

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

    It is not the case that If P = NP, then 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.Hartmanis and Stearns (1965) grounded complexity in resource-bounded computation where 'no harder than' requires a precise reduction type, but the claim leaves the reduction unspecified.
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    • 2.Without specifying whether the reduction is many-one, Turing, or Cook, the comparative difficulty relation invoked is semantically underdetermined and cannot bear the logical weight the argument assigns it.
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    • 3.Cook's original 1971 formalization treats SAT's hardness relative to NP-completeness, not relative to truth table enumeration, making the chosen baseline philosophically unmotivated.
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    Reason for 2 of 2
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    • 1.Constructing a truth table is exponential in the number of variables, not polynomial, so it cannot serve as the baseline for 'no harder than'.
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    • 2.The claim conflates asymptotic complexity classes with concrete algorithmic equivalence: P=NP would mean SAT is solvable in polynomial time, making it strictly easier than truth table construction, not equally hard.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.P is the class of problems decidable efficiently
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    • 2.NP is the class of problems verifiable efficiently given a certificate
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    • 3.If P = NP, deciding and verifying coincide up to a polynomial factor for all NP problems
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    Explore the most compelling reason on the other side.