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    The feasibility thesis equates 'polynomial time' with tra... — Carmelics
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    Challenges→The RAM machine model does not provide an asymptotically superior model of feasible computation compared to the Turing machine model.

    The feasibility thesis equates 'polynomial time' with tractability, but this conflation (criticized by Parberry, Gurevich) smuggles in an empirical claim as a definitional truth.

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    Reasons For

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    Reason for
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    • 1.Polynomial algorithms with huge constants (e.g., O(n^100)) are theoretically tractable but practically intractable on realistic inputs.
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    • 2.The P vs NP problem's significance derives from open empirical questions about algorithm speedups, not settled mathematical definitions.
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    • 3.Conflating definitional equivalence with empirical adequacy obscures why polynomial-time serves as a useful heuristic rather than fundamental truth.
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    Reasons Against

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    • 1.Polynomial-time is not presented as 'tractable' by most theorists but as a principled mathematical threshold independent of empirical validation.
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    • 2.Practical hardness depends on problem instances and hardware; defining tractability by polynomial time avoids problem-specific empiricism.
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    • 3.The feasibility thesis succeeds because polynomial algorithms typically outperform exponential ones across computational domains studied in practice.
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    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    Conflating definitional equivalence with empirical adequacy obscures why polynom...Polynomial algorithms with huge constants (e.g., O(n^100)) are theoretically tra...Polynomial-time is not presented as 'tractable' by most theorists but as a princ...Practical hardness depends on problem instances and hardware; defining tractabil...
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    The P vs NP problem's significance derives from open empirical questions about a...The RAM machine model does not provide an asymptotically superior model of feasi...The feasibility thesis succeeds because polynomial algorithms typically outperfo...

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