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    Home/Original/inverse
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    Inverse View

    It is not the case that Hartmanis and Stearns (1965) grounded complexity in resource-bounded computation where 'no harder than' requires a precise reduction type, but the claim leaves the reduction unspecified.

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    Reasons For

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    Reason for
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    • 1.An unspecified reduction type makes 'no harder than' meaningless; different reductions yield contradictory complexity orderings between problems.
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    • 2.By 1965, standard reductions were established in computability theory; failing to specify them suggests incomplete theoretical work rather than principled generality.
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    • 3.Ambiguity about reduction types permitted ad-hoc reasoning and hindered reproducibility—problems that plagued early complexity theory until P vs NP clarified stakes.
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    Reasons Against

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    Reason against
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    • 1.Hartmanis-Stearns advanced theory by anchoring complexity to measurable resources (time/space), moving beyond informal intuitions about difficulty.
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    • 2.Leaving reduction types unspecified preserved generality, allowing the framework to accommodate multiple valid formalizations (Turing, oracle, polynomial-time reductions).
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    • 3.The vagueness reflected genuine mathematical uncertainty about which reductions capture 'no harder than' conceptually, not mere oversight.
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