On Higher Arthur-Merlin Classes

We study higher Arthur-Merlin classes de ned via several natural probabilistic operators BP;R and co-R. We investigate the complexity classes they de ne, and a number of interactions between these operators and the standard polynomial time hierarchy. We prove a hierarchy theorem for these higher Arthur-Merlin classes involving interleaving operators, and a theorem giving non-trivial upper bounds to the intersection of the complementary classes in the hierarchy.