Randomized algorithms
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
A new bound on the size of the largest critical set in a Latin square
Discrete Mathematics - Special issue: Combinatorics 2000
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We show that each randomized o(|G|^2)-query algorithm can recover only an expected o(1) fraction of the Cayley table of some finite Abelian loop (G,@?), where both multiplication and inversion queries are allowed. Furthermore, each randomized o(|R|^2)-query algorithm can recover only an expected o(1) fraction of any of the Cayley tables of some finite commutative semiring (R,+,@?), with (R,+) being a commutative aperiodic monoid, where each query may ask for x+y or x@?y for any x, y@?R.