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    Feasibility is an empirical and engineering concept tied ... — Carmelics
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    Challenges→Possession of a polynomial time decision algorithm is sufficient grounds for regarding a problem as feasibly decidable.

    Feasibility is an empirical and engineering concept tied to actual resource constraints, not an abstract worst-case asymptotic property.

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    Reasons For

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    Reason for
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    • 1.Real-world systems operate under finite budgets (time, memory, energy). Asymptotic analysis ignores these hard constraints engineers actually face.
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    • 2.Algorithm A may be O(n²) but run in milliseconds on current hardware; Algorithm B may be O(n log n) but require unavailable resources. Feasibility requires empirical validation.
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    • 3.Theoretical worst-case bounds often don't occur in practice. Average-case and typical performance matter more for actual deployment decisions.
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    Reasons Against

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    • 1.Asymptotic properties predict how algorithms *scale* as problems grow. Today's feasible problem may become infeasible tomorrow—only asymptotics capture this.
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    • 2.Hardware improves, but exponential algorithms eventually outpace it. Polynomial bounds remain feasible; exponential ones don't. This isn't empirical—it's mathematical.
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    • 3.Confusing feasibility with current empirical performance risks building systems that fail catastrophically when inputs exceed tested ranges or resources decrease.
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    Related

    Algorithm A may be O(n²) but run in milliseconds on current hardware; Algorithm ...Asymptotic properties predict how algorithms *scale* as problems grow. Today's f...Confusing feasibility with current empirical performance risks building systems ...Hardware improves, but exponential algorithms eventually outpace it. Polynomial ...
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    Possession of a polynomial time decision algorithm is sufficient grounds for reg...Real-world systems operate under finite budgets (time, memory, energy). Asymptot...Theoretical worst-case bounds often don't occur in practice. Average-case and ty...

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