Verification of Identities

@article{Rajagopalan2000VerificationOI,
  title={Verification of Identities},
  author={Sridhar Rajagopalan and Leonard J. Schulman},
  journal={SIAM J. Comput.},
  year={2000},
  volume={29},
  pages={1155-1163}
}
We provide an O(n2 log 1 δ ) time randomized algorithm to check whether a given operation ◦ : S × S → S is associative (where n = |S| and δ > 0 is the error probability required of the algorithm). We prove that (for any constant δ) this performance is optimal up to a constant factor, even if the operation is “cancellative.” No sub-n3 time algorithm was previously known for this task. More generally we give an O(nc) time randomized algorithm to check whether a collection of c-ary operations… CONTINUE READING

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