6. The Size of Randomized Polynomial Time

Abstract

This is the first chapter where we will give arguments about the frequency of occurrence of certain languages in order to separate complexity classes. The particular framework we will use is that of resource-bounded measure. The formalism turns to be well-suited to study the BPP versus EXP problem. In this chapter, we will show that either randomized polynomial time coincides with exponential time or else it is a small subclass of exponential time in the sense of resource-bounded measure. We will see more applications to the BPP versus EXP problem in the next two chapters.