Relations between average-case and worst-case complexity

The consequences of the worst-case assumption NP = P are very well understood. On the other hand, we only know a few consequences of the average-case assumption "NP is easy on average." In this paper we establish several new results on the worst-case complexity of Arthur-Merlin games (the class AM) under the average-case complexity assumption "NP is easy on average." We first consider a stronger notion of "NP is easy an average" namely NP is easy on average with respect to distributions that are computable by a polynomial size circuit family. Under this assumption we show: - AM subset of NSUBEXP. Under the assumption that NP is easy on average with respect to poly-nomial-time computable distributions, we show: - AME = E where AME is the exponential version of AM. This improves an earlier known result that if NP is easy on average then NE = E. For every c > 0, AM subset of [io-pseudo(NTIME(nc))]-NP, Roughly this means that for any language L in AM there is a language L' in NP so that it is computationally infeasible to distinguish L from L'.