Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    If factorization witnesses were unpolynomially sized, coN... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→A coNP witness must be both unique-enough to be convincing and polynomially bounded in size; the prime factorization of n can require exponentially many bits relative to log n when n has many small factors.

    If factorization witnesses were unpolynomially sized, coNP ≠ NP would follow trivially; this contradicts that the P vs NP question remains open, suggesting the premise oversimplifies the structural issue.

    ?Rate how convincing each reason is below to see the overall strength.

    No one has weighed in yet. Be the first to share reasons for or against this statement.

    Sign in or register to share your perspective on this statement.

    Key Terms

    FACTORIZATION(Used as an example of a problem in NP ∩ coNP not currently known to be in P.)
    The computational problem: given ⟨n,m⟩, does n have a factor d with 1 < d ≤ m?
    NP
    The class of problems for which membership can be verified efficiently once an appropriate certificate is provided.
    Open question (in mathematics/philosophy)(as used in mathematics and logic)
    A question that hasn't been answered yet, despite significant effort by experts.
    P vs NP question(as used in computer science and mathematics)
    One of math and computer science's biggest unsolved mysteries: whether problems that are hard to solve are also hard to check, or whether checking can be much faster than solving.
    Polynomial/Polynomially sized(as used in computer science complexity theory)

    Next step

    Based on where you are in your exploration

    Explore a random proposition
    Start fresh with something unrelated.
    Growing at a manageable, predictable rate as numbers get bigger (roughly, doubling the input doesn't cause the size to explode exponentially).
    Witness (in computational complexity)(as used in computer science)
    A piece of evidence or proof that confirms something is true—in this case, proof that a number can be broken into factors.
    coNP(Complement class of NP; defined via universal quantification over polynomial-bounded witnesses.)
    A problem X is in coNP just in case there exists a polynomial-decidable relation R(x,y) and a polynomial p(x) such that x ∈ X if and only if ∀y ≤ p(|x|) R(x,y).

    Connections

    1 linked claim

    A coNP witness must be both unique-enough to be convincing and polynomially boun...

    Related

    A coNP witness must be both unique-enough to be convincing and polynomially boun...

    Details

    Type
    premise
    Perspectives
    0 (0 for, 0 against)

    Open for perspectives

    This idea is waiting for its first supporting or challenging perspective.

    Share the first perspective