We show that several reducibility notions coincide when applied to the Graph Isomorphism (GI) problem. In particular we show that if a set is many-one logspace reducible to GI, then it is in fact many-one AC 0 reducible to GI. For the case of Turing reducibilities we show that for any k ≥ 0 an NC k + 1 reduction to GI can be transformed into an AC k reduction to the same problem.


Computational complexity reducibilities graph isomorphism 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jacobo Torán
    • 1
  1. 1.Institut für Theoretische Informatik, Universität Ulm, D-89069 UlmGermany

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