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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that Practical computability correlates with the existence of polynomial time algorithms.

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Cobham-Edmonds thesis conflates worst-case complexity with practical performance, ignoring average-case and fixed-parameter tractability.
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    • 2.Many exponential-time algorithms (e.g., simplex method) perform efficiently in practice, while some polynomial algorithms (e.g., ellipsoid method) are practically useless.
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    • 3.The correlation between polynomial-time solvability and practical computability is an empirical generalization, not a conceptual truth, and admits systematic counterexamples.
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    Reason for 2 of 2
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    • 1.Our current inability to prove P≠NP means the boundary between polynomial and super-polynomial algorithms reflects epistemic, not ontological, limits on computation.
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    • 2.A claim grounded in the absence of discovered polynomial algorithms conflates the sociology of mathematical discovery with structural facts about computational complexity.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.In cases where a function can be uniformly computed for practically relevant inputs, a polynomial time algorithm implementable on current hardware has typically been discovered.
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    • 2.In cases where uniform computation is not currently possible, a polynomial time algorithm has typically not been discovered, and circumstantial evidence often suggests none can exist.
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