Abstract
The authors provide an ?(n2) time randomized algorithm to check whether a given operation f: S x S → S is associative (letting n=|S|). They prove this performance is optimal (up to polylogarithmic factors) even in case the operation is "cancellative". No sub-n3 algorithm was previously known for this task. More generally they give an O(n3) time randomized algorithm to check whether a collection of c-ary operations satisfy any given "read-once" identity.