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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that The existence of a polynomial time algorithm for any single NP-complete problem would entail the existence of polynomial time algorithms for all problems in NP.

    ?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 existence of a polynomial-time algorithm is a modal claim about computability, not a demonstrated constructive fact, and modal existence does not transfer across reductions without preserving algorithmic structure.
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      Think about whether this reason is strong or weak

    • 2.Polynomial-time reducibility preserves decision-problem solvability in principle, but the reduction itself may introduce constant or hidden complexity factors that render the composed algorithm impractical even if formally polynomial.
      ?

      Think about whether this reason is strong or weak

    • 3.Hartmanis and Stearns's foundational work shows complexity classes are defined relative to machine models, so 'polynomial time' is not a robust absolute property immune to variation in computational substrate.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.The inference from 'a polynomial algorithm exists for one NP-complete problem' to 'polynomial algorithms exist for all NP problems' treats existence as a transferable property, but Kripkean possible-worlds semantics demands we specify in which worlds and under which interpretations such algorithms exist.
      ?

      Think about whether this reason is strong or weak

    • 2.The supporting argument's transitivity premise holds for decision problems under standard Turing reductions, but Ladner's theorem demonstrates that if P≠NP there exist problems in NP neither in P nor NP-complete, complicating the universality of the entailment.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The polynomial-time reducibility relation is transitive.
      ?

      Think about whether this reason is strong or weak

    • 2.NP-complete problems are defined such that every problem in NP is polynomial-time reducible to them.
      ?

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