Proceedings of 37th Conference on Foundations of Computer Science (1996)
Oct. 14, 1996 to Oct. 16, 1996
S. Rajagopalan , Princeton Univ., NJ, USA
L.J. Schulman , Princeton Univ., NJ, USA
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.
randomised algorithms; identity verification; time randomized algorithm; associative operation; optimal performance; c-ary operations; read-once identity
S. Rajagopalan and L. Schulman, "Verifying identities," Proceedings of 37th Conference on Foundations of Computer Science(FOCS), Burlington, VT, 1996, pp. 612.