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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that If any NP-complete problem has a polynomial time algorithm, then all problems in NP have polynomial time algorithms

    ?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.The claim presupposes a fixed, language-independent notion of 'polynomial time' that ignores relativization results (Baker-Gill-Solovay 1975).
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    • 2.Oracles exist relative to which P=NP and others relative to which P≠NP, showing the claim's proof must transcend relativizable methods.
      ?

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    • 3.No currently known proof technique for complexity separations is non-relativizing, so the conditional claim lacks a coherent proof-theoretic foundation.
      ?

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    Reason for 2 of 2
    ?
    • 1.Reduction-based arguments assume that computational problems have determinate, mind-independent identity conditions across different encodings.
      ?

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    • 2.Wittgensteinian and Kripkean considerations about rule-following suggest that 'same problem' across reductions is interpretation-relative, not intrinsic.
      ?

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    • 3.If problem identity is encoding-relative, polynomial-time reducibility ≤_P does not transitively preserve the property of being 'the same computational task'.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Polynomial-time reducibility ≤_P is transitive
      ?

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    • 2.Every problem in NP is polynomial-time reducible to any NP-complete problem
      ?

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