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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that Hartmanis and Stearns' original 1965 framework acknowledged that asymptotic analysis abstracts away practically critical constant factors and thresholds.

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    Reasons For

    1 perspective
    Reason for
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    • 1.The claim overstates acknowledgment: their 1965 paper focused on defining computability classes, not critiquing constant-factor abstraction.
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    • 2.Modern complexity theory often obscures that polynomial algorithms with large constants can be impractical, misleading practitioners about solvability.
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    • 3.Ignoring thresholds has real consequences: an O(n³) algorithm with huge constants may outperform O(n log n) only beyond infeasible input sizes.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Hartmanis-Stearns explicitly defined complexity classes relative to machine models, acknowledging that constants depend on implementation choices.
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    • 2.Their framework enabled tractability distinctions (P vs NP) that remain useful despite ignoring constants, validating the abstraction's value.
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    • 3.Asymptotic analysis was presented as a tool for theoretical understanding, not as a complete model of practical runtime behavior.
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