Testing Commutativity of a Group and the Power of Randomization
نویسنده
چکیده
Let G be a group generated by k elements G = ⟨g1, . . . , gk⟩, with group operations (multiplication, inversion, comparison with id) performed by a black box. We prove that one can test whether the group G is abelian at a cost of O(k) group operations. On the other hand, we show that deterministic approach requires Ω(k) group operations.
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تاریخ انتشار 2000