STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Linear time algorithms for Abelian group isomorphism and related problems
Journal of Computer and System Sciences
Quantum property testing of group solvability
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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The authors provide an 脮(n2) time randomized algorithm to check whether a given operation f: S x S 驴 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.