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    The AKS verification of primality operates on the bit-len... — Carmelics
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    Challenges→FACTORIZATION is in coNP

    The AKS verification of primality operates on the bit-length of each factor, but the product of these lengths can grow super-polynomially relative to the input encoding of n.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.AKS checks divisibility by polynomials over Z/nZ, requiring bit operations proportional to log(n)² or higher per polynomial test.
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    • 2.The number of distinct prime power factors can be O(log n), and encoding each factor's bit-length independently yields multiplicative complexity.
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    • 3.Complexity analysis distinguishes between input size (log n bits) and actual computational work across factor encodings, which can diverge.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.AKS runtime is proven polynomial in log(n)—O((log n)⁶) or O((log n)⁴) with improvements—making super-polynomial growth impossible by definition.
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    • 2.A product of factor bit-lengths is still bounded by O((log n)²), not exceeding the polynomial bound relative to input encoding length.
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    • 3.The claim conflates bit-operations on individual factors with overall algorithmic complexity, which must remain polynomial for AKS correctness.
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    Connections

    1 linked claim · 2 topics

    Proof of definition segments1 linkedTruth & Knowledge1 linked
    FACTORIZATION is in coNP

    Related

    A product of factor bit-lengths is still bounded by O((log n)²), not exceeding t...AKS checks divisibility by polynomials over Z/nZ, requiring bit operations propo...AKS runtime is proven polynomial in log(n)—O((log n)⁶) or O((log n)⁴) with impro...Complexity analysis distinguishes between input size (log n bits) and actual com...
    +3 moreShow less
    FACTORIZATION is in coNPThe claim conflates bit-operations on individual factors with overall algorithmi...The number of distinct prime power factors can be O(log n), and encoding each fa...

    Details

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