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    The existence of a polynomial-time algorithm is a modal c... — Carmelics
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    Challenges→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.

    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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    Key Terms

    Modal claim(logic/philosophy)
    A statement about what is necessary (must be true), possible (could be true), or impossible (cannot be true), rather than just what is actually true in one situation.
    algorithmic structure(computer science)
    The specific way a procedure is organized and how it works—the details of its step-by-step process, not just what problem it solves.
    computability(computer science and philosophy of mathematics)
    The study of what problems can or cannot be solved by following a step-by-step procedure (algorithm) on a computer.
    constructive fact(epistemology and philosophy of mathematics)
    Something that is explicitly shown or built to exist through a concrete demonstration, rather than merely claimed to exist in theory.
    modal existence

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    (metaphysics and logic)
    The idea that something is possible or could exist, as opposed to the claim that it actually exists right now.
    polynomial-time algorithm(computer science/computability)
    A step-by-step procedure for solving a problem that runs reasonably fast on a computer—the number of steps needed grows at a manageable rate as the problem gets bigger.
    reductions(computer science and logic)
    Transformations that convert one problem into another to show they have similar difficulty—like proving two puzzles are equally hard by showing how to solve one if you can solve the other.

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    2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked

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    The existence of a polynomial time algorithm for any single NP-complete problem ...

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