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Graph isomorphism is low for PP

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STACS 92 (STACS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 577))

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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.

This research was supported by the DAAD (Acciones Integradas 1991, 313-AI-e-es/zk). A full verstion of this paper is available as Ulmer Informatik-Bericht Nr. 91-04.

Research partially supported by ESPRIT-II Basic Research Actions Program of the EC under Contract No. 3075 (project ALCOM)

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Alain Finkel Matthias Jantzen

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© 1992 Springer-Verlag Berlin Heidelberg

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Köbler, J., Schöning, U., Torán, J. (1992). Graph isomorphism is low for PP. In: Finkel, A., Jantzen, M. (eds) STACS 92. STACS 1992. Lecture Notes in Computer Science, vol 577. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55210-3_200

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  • DOI: https://doi.org/10.1007/3-540-55210-3_200

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  • Print ISBN: 978-3-540-55210-9

  • Online ISBN: 978-3-540-46775-5

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