BPP and the polynomial hierarchy

Abstract

BPP is the class of all sets that can be divided by a probabilistic Turing machine with bounded error probability within a polynomial time bound. Sipser (1983) showed that BPP is contained in the polynomial hierarchy of Meyer and Stockmeyer. In this paper it is shown by pure counting arguments that BPP is contained in ΣP2, the second level of the hierarchy. © 1983.