<P> Together, AvgP and distNP define the average - case analogues of P and NP, respectively . </P> <P> Let (L, D) and (L', D') be two distributional problems . (L, D) average - case reduces to (L', D') (written (L, D) ≤ (L', D')) if there is a function f that for every n, on input x can be computed in time polynomial in n and </P> <Ol> <Li> (Correctness) x ∈ L if and only if f (x) ∈ L' </Li> <Li> (Domination) There are polynomials p and m such that, for every n and y, ∑ x: f (x) = y D n (x) ≤ p (n) D m (n) ′ (y) (\ displaystyle \ sum \ limits _ (x: f (x) = y) D_ (n) (x) \ leq p (n) D'_ (m (n)) (y)) </Li> </Ol> <Li> (Correctness) x ∈ L if and only if f (x) ∈ L' </Li>

What is average case analysis of an algorithm