computational complexity

, Volume 2, Issue 4, pp 301–330

Graph isomorphism is low for PP

  • Johannes Köbler
  • Uwe Schöning
  • Jacobo Torán
Article

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 an oracle. Furthermore, we show that graph isomorphism belongs to the class LWPP (see Fenner, Fortnow, Kurtz [12]). 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.

Key words

graph isomorphism complexity classes lowness counting properties 

Subject classifications

68Q15 68Q25 05C60 68R10 

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Copyright information

© Birkhäuser Verlag 1992

Authors and Affiliations

  • Johannes Köbler
    • 1
  • Uwe Schöning
    • 1
  • Jacobo Torán
    • 2
  1. 1.Theoretische InformatikUniversität Ulm Oberer EselsbergUlmGermany
  2. 2.Departamento L.S.I.Universitat Politècnica de CatalunyaBarcelonaSpain

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