Graph isomorphism is low for ZPP(NP) and other lowness results

Abstract

We show the following new lowness results for the probabilistic class ZPPNP. -The class AM ∩ coAM is low for ZPPNP. As a consequence it follows that Graph Isomorphism and several group-theoretic problems known to be in AM ∩ coAM are low for ZPPNP. -The class IP[P=poly], consisting of sets that have interactive proof systems with honest provers in P=poly, is also low for ZPPNP. We consider lowness properties of nonuniform function classes, namely, NPMV=poly, NPSV=poly, NPMVt=poly, and NPSVt=poly. Specifically, we show that -Sets whose characteristic functions are in NPSV=poly and that have program checkers (in the sense of Blum and Kannan [8]) are low for AM and ZPPNP. -Sets whose characteristic functions are in NPMVt=poly are low for Σp2.