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Testing commutativity of a group and the power of randomization

  • Igor Pak (a1)
Abstract

Let 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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References
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LMS Journal of Computation and Mathematics
  • ISSN: -
  • EISSN: 1461-1570
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