Graph Isomorphism is Low for PP

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 di cult) 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 classi cations. 68Q15, 68Q25, 05C60, 68R10.

• Type: Conference
• Year: 1992
• Where: STACS
• Authors: Johannes Köbler, Uwe Schöning, Jacobo Torán
• Keywords: Graph Isomorphism, Graph Isomorphism Problem, Problem Group Factorization, STACS 1992, Theoretical Computer Science