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    The claim conflates decision-problem complexity with the ... — Carmelics
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    Challenges→If P equals NP, factoring a natural number would be no more difficult than verifying that a given factorization is correct

    The claim conflates decision-problem complexity with the search problem of producing a factorization, which require separate complexity-theoretic treatment.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Decision problems (yes/no answers) and search problems (finding solutions) have fundamentally different computational structures requiring distinct analysis.
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    • 2.Verifying a factorization is polynomial-time while finding one may be hard; conflating these obscures this crucial asymmetry.
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    • 3.NP-completeness applies to decision problems, not search; treating factorization as a decision problem misses search-specific hardness results.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Decision and search versions of factorization reduce to each other via standard techniques; distinguishing them is merely notational convenience.
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    • 2.Hardness of factorization (in practice and theory) comes from the same underlying structure whether framed as decision or search—the distinction is artificial.
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    • 3.Cryptographic security depends on search difficulty; insisting on separate treatment obscures that both versions capture the same computational barrier.
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    Related

    Cryptographic security depends on search difficulty; insisting on separate treat...Decision and search versions of factorization reduce to each other via standard ...Decision problems (yes/no answers) and search problems (finding solutions) have ...Hardness of factorization (in practice and theory) comes from the same underlyin...
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    If P equals NP, factoring a natural number would be no more difficult than verif...NP-completeness applies to decision problems, not search; treating factorization...Verifying a factorization is polynomial-time while finding one may be hard; conf...

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    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit