Error-bounded probabilistic computations between MA and AM

Abstract

We introduce the probabilistic complexity class SBP. This class emerges from BPP by keeping the promise of a probability gap but decreasing the probability limit to exponentially small values. We locate SBP in the polynomial-time hierarchy, more precisely, between MA and AM. We provide evidence that SBP does not coincide with these and other known complexity classes. We construct an oracle relative to which SBP is not contained in Σ2P. We provide a new characterization of BPPpath. This characterization shows that SBP is a subset of BPPpath. Consequently, there is an oracle relative to which BPPpath is not contained in Σ2P. © Springer-Verlag Berlin Heidelberg 2003.