Testing commutativity of a group and the power of randomization
2012 ◽
Vol 15
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pp. 38-43
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AbstractLet G be a group generated by k elements, G=〈g1,…,gk〉, with group operations (multiplication, inversion and comparison with identity) 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 a deterministic approach requires Ω(k2) group operations.
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2010 ◽
Vol 09
(02)
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pp. 241-256
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1999 ◽
Vol 173
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pp. 249-254
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1969 ◽
Vol 27
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pp. 6-7
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1980 ◽
Vol 38
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pp. 30-33
2005 ◽
Vol 19
(3)
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pp. 129-132
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