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.
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).