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    Hartmanis and Stearns (1965) grounded complexity in resou... — Carmelics
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    Challenges→If P = NP, then finding a satisfying valuation for a propositional formula would be no harder than constructing its truth table

    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.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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    Reasons Against

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    Reason against
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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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    Key Terms

    Complexity (in computation)(as the main subject of the statement)
    A measure of how many resources—like time or memory—a computer needs to solve a problem. Simple problems use fewer resources; complex problems use more.
    Hartmanis and Stearns(as founders of computational complexity theory)
    Two computer scientists who developed an important framework for understanding how much computational effort (time or memory) different types of problems require to solve.
    No harder than(as the comparative phrase being made precise)
    A way of comparing difficulty between two problems—saying problem A is 'no harder than' problem B means A is at least as easy as B, possibly easier.
    Reduction (in logic and computation)(as the technical tool for comparing problem difficulty)
    A method of solving one problem by converting it into another problem you already know how to solve. It shows that if you can solve problem B, you can also solve problem A.
    Reduction type(as what needs to be precise in complexity comparisons)
    A specific set of rules for how you're allowed to convert one problem into another—different types allow different kinds of conversions, making the comparison more or less strict.
    resource-bounded computation(DRT's account of why human agents fail to be logically omniscient)
    Reasoning or inference performed by agents who have limited cognitive resources and therefore cannot derive all logical consequences of their representations

    Connections

    2 topics

    Proof of definition segments1 linkedTruth & Knowledge1 linked

    Related

    Ambiguity about reduction types permitted ad-hoc reasoning and hindered reproduc...An unspecified reduction type makes 'no harder than' meaningless; different redu...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit
    By 1965, standard reductions were established in computability theory; failing t...
    Hartmanis-Stearns advanced theory by anchoring complexity to measurable resource...
    +3 moreShow less
    If P = NP, then finding a satisfying valuation for a propositional formula would...Leaving reduction types unspecified preserved generality, allowing the framework...The vagueness reflected genuine mathematical uncertainty about which reductions ...