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.
Cite
CITATION STYLE
Köbler, J., Schöning, U., & Torán, J. (1992). Graph isomorphism is low for PP. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 577 LNCS, pp. 401–411). Springer Verlag. https://doi.org/10.1007/3-540-55210-3_200
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