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    The Cobham-Edmonds Thesis conflates mathematical tractabi... — Carmelics
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    Challenges→The complexity class P describes the class of feasibly decidable problems

    The Cobham-Edmonds Thesis conflates mathematical tractability with physical feasibility by ignoring the magnitude of polynomial constants and exponents.

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    Reasons For

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    Reason for
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    • 1.A polynomial algorithm with exponent 100 is computationally infeasible despite being 'tractable' by complexity theory standards.
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    • 2.Physical constraints (time, energy, hardware limits) depend on actual constants, not just asymptotic behavior as n→∞.
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    • 3.Complexity classes conflate theoretical computability with practical solvability, misleading resource allocation in engineering.
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    Reasons Against

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    • 1.The thesis distinguishes feasibility classes precisely because polynomial-time algorithms typically have reasonable constants in practice.
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    • 2.Exponential algorithms are uniformly worse across problem instances; polynomial algorithms scale differently, making the distinction meaningful.
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    • 3.Criticizing P for ignoring constants conflates descriptive theory with prescriptive engineering—they serve different purposes.
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    Proof of definition segments1 linkedTruth & Knowledge1 linked

    Related

    A polynomial algorithm with exponent 100 is computationally infeasible despite b...Complexity classes conflate theoretical computability with practical solvability...Criticizing P for ignoring constants conflates descriptive theory with prescript...Exponential algorithms are uniformly worse across problem instances; polynomial ...
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    Physical constraints (time, energy, hardware limits) depend on actual constants,...The complexity class P describes the class of feasibly decidable problemsThe thesis distinguishes feasibility classes precisely because polynomial-time a...

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