A Nonadaptive NC Checker for Permutation Group Intersection

In this paper we design a nonadaptive NC checker for permutation group intersec tion sharpening a result from Blum and Kannan This is a consequence of two results First we show that a nontrivial permutation in the intersection of two given permutation groups described by lists of generators can be computed by an NC algo rithm with one round of parallel queries to the Group Intersection problem Next we design a two round interactive proof system for the complement of the Group Intersec tion problem for which the honest prover can be simulated by an NC algorithm with one round of parallel queries to Group Intersection As a consequence we also have nonadaptive NC checkers for some related group theoretic problems On the technical side we de ne a generalization of wreath products of permutation groups This product plays a crucial role in the design of the nonadaptive checkers