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Graph isomorphism is low for PP

  • Johannes Köbler
  • Uwe Schöning
  • Jacobo Torán
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 577)

Abstract

We show that the graph isomorphism problem is low for PP and for C=P, i.e. it does not provide a PP or C=P computation with any additional power when used as oracle. Furthermore, we show that graph isomorphism belongs to the class LWPP (see Fenner, Fortnow, Kurtz [FeFoKu 91]). A similar result holds for the (apparently more difficult) problem Group Factorization. The problem of determining whether a given graph has a nontrivial automorphism, Graph Automorphism, is shown to be in SPP, and is therefore low for PP, C=P, and ModkP, k≥2.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Johannes Köbler
    • 1
  • Uwe Schöning
    • 1
  • Jacobo Torán
    • 2
  1. 1.Theoretische InformatikUniversität UlmUlmGermany
  2. 2.Departamento L.S.I.U. Politecnica de CatalunyaBarcelonaSpain

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