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    Home/Original/inverse
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    Inverse View

    It is not the case that In complexity theory, feasibility is a property of time complexity functions or their rates of growth, not of individual natural numbers.

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Feasibility judgments in practice are always made relative to specific input sizes, not abstract growth functions.
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    • 2.An algorithm with O(n^2) complexity may be infeasible for n=10^18 yet feasible for n=100, making the individual value decisive.
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    • 3.Hartmanis and Stearns' original 1965 framework acknowledged that asymptotic analysis abstracts away practically critical constant factors and thresholds.
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    Reason for 2 of 2
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    • 1.Gurevich and Shelah's work on feasibility demonstrates that polynomial-time classification fails to track actual computational resource bounds in finite domains.
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    • 2.If feasibility is purely a property of growth functions, then no fact about any individual natural number can bear on whether a computation is feasible, which is computationally absurd.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.To apply the Cobham-Edmonds Thesis and judge whether a problem X is feasibly decidable, one considers the order of growth of the time complexity t(n) of the most efficient algorithm for deciding X.
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    • 2.This analysis applies to functions of type ℕ → ℕ and their rates of growth, not to individual values of n.
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