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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that FACTORIZATION is in NP ∩ coNP simultaneously

    Aggregate Confidence:0%

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Membership proofs for NP require a verifiable witness, but FACTORIZATION's complement requires certifying the *absence* of non-trivial factors, which standard NP witnesses cannot directly encode.
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      Think about whether this reason is strong or weak

    • 2.Pratt's primality certificates establish coNP membership for PRIMES only because of deep number-theoretic structure; analogous certificates for composite numbers with *all* factor pairs are not obviously constructible in polynomial-length form.
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      Think about whether this reason is strong or weak

    • 3.Claiming NP ∩ coNP membership conflates the existence of efficient verification with the existence of succinct, universally accepted certificate schemes, which for FACTORIZATION remains an open constructive question.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.The intersection NP ∩ coNP is a syntactic complexity class defined relative to a fixed computational model; FACTORIZATION as a decision problem (does n have a factor ≤ k?) differs structurally from the search problem, and membership claims must specify which formulation is at issue.
      ?

      Think about whether this reason is strong or weak

    • 2.Hartmanis and Hopcroft's framework for structural complexity treats class membership as a property of formal languages, not of mathematical problems per se, so asserting FACTORIZATION 'is in' NP ∩ coNP without specifying the encoding and decision variant commits a use-mention conflation.
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      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.FACTORIZATION is in NP
      ?

      Think about whether this reason is strong or weak

    • 2.FACTORIZATION is in coNP
      ?

      Think about whether this reason is strong or weak

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