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    Feasibility judgments in practice are always made relativ... — Carmelics
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    Challenges→In complexity theory, feasibility is a property of time complexity functions or their rates of growth, not of individual natural numbers.

    Feasibility judgments in practice are always made relative to specific input sizes, not abstract growth functions.

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    Reasons For

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    • 1.Real engineering decisions require concrete thresholds: an O(n²) algorithm is acceptable for n<10⁶ but infeasible for n=10⁹, making growth rates alone insufficient.
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    • 2.Asymptotic analysis ignores constant factors and implementation details that dominate performance at practical problem sizes, misleading practitioners about actual feasibility.
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    • 3.Systems operate within fixed computational budgets (memory, time, power), making input-size-specific feasibility judgments necessary for responsible resource allocation.
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    Reasons Against

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    • 1.Growth functions precisely capture how feasibility *changes with scale*; dismissing them privileges anecdotal problem sizes over principled reasoning about scaling limits.
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    • 2.Without abstract growth analysis, practitioners cannot distinguish temporary bottlenecks from fundamental scalability failures, reducing their ability to anticipate future constraints.
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    • 3.Feasibility judgments tied only to current input sizes become outdated as data volumes grow; growth functions provide durable guidance across changing practical contexts.
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    Related

    Asymptotic analysis ignores constant factors and implementation details that dom...Feasibility judgments tied only to current input sizes become outdated as data v...Growth functions precisely capture how feasibility *changes with scale*; dismiss...In complexity theory, feasibility is a property of time complexity functions or ...
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    Real engineering decisions require concrete thresholds: an O(n²) algorithm is ac...Systems operate within fixed computational budgets (memory, time, power), making...Without abstract growth analysis, practitioners cannot distinguish temporary bot...

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