4.1 Introduction 4.2 Boolean Function Evalutation Figure 4.2.1: a Depth 2k And-or Circuit

In this lecture, we will first consider the problem of boolean function evaluation and prove that randomized algorithms (in the expected case) perform better than deterministic algorithms. The boolean circuits that we consider, can be naturally extended to obtain a game tree. We will then state Von Neumann’s minimax theorem and its extension Yao’s principle. Finally, we show how Yao’s principle can be used to obtain lower bounds on the expected running time of randomized algorithms.