Arthur-Merlin games and the problem of isomorphism testing

Authors:
Jacobo Torán
Affiliations:
Abt. Theoretische Informatik, Universität Ulm, Ulm, Germany
Venue:
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Year:
2005

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Abstract

We survey some recent results related to the complexity of isomorphism testing in different algebraic structures. We concentrate on isomorphism problems for finite groups and rings. The complexity of these problems depends not only on the particular underlying algebraic structure, but also on the way the input instances are encoded. As in the case of better studied isomorphism questions, like graph isomorphism, Arthur-Merlin games provide a good tool for proving upper bounds for these problems in terms of complexity classes. We consider questions related to the number of random and nondeterministic bits used in the Arthur-Merlin protocols for isomorphism testing as well as the derandomization of these protocols.