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. © 1992 Birkhäuser Verlag.
CITATION STYLE
Köbler, J., Schöning, U., & Torán, J. (1992). Graph isomorphism is low for PP. Computational Complexity, 2(4), 301–330. https://doi.org/10.1007/BF01200427
Mendeley helps you to discover research relevant for your work.