Complexity of Ring Morphism Problems

@article{Kayal2006ComplexityOR,
  title={Complexity of Ring Morphism Problems},
  author={Neeraj Kayal and Nitin Saxena},
  journal={computational complexity},
  year={2006},
  volume={15},
  pages={342-390}
}
Abstract.We study the complexity of the isomorphism and automorphism problems for finite rings. We show that both integer factorization and graph isomorphism reduce to the problem of counting automorphisms of a ring. This counting problem is shown to be in the functional version of the complexity class AM ∩ coAM and hence is not NP-complete unless the polynomial hierarchy collapses. As a “positive” result we show that deciding whether a given ring has a non-trivial automorphism can be done in… CONTINUE READING

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