A second step toward the strong polynomial-time hierarchy

Abstract

In this paper we discuss the concepts ofimmunity andsimplicity in levels of the relativized Polynomial-time Hierarchy just aboveP. We consider various diagonalization techniques with which oracle sets can be constructed relative to which strong separations between language classes in the first two levels of this hierarchy are established. In particular, we build oracle sets for separation of relativized Σ2P from relativizedNP with immunity, of relativized Σ2P from relativizedNP with bi-immunity, of relativized Σ2P from relativized Δ2P with immunity, of relativized Π2P from relativized Δ2P with immunity, and finally of relativized Σ2P from relativized Π2P with simplicity.