Interactive information complexity

Abstract

The primary goal of this paper is to define and study the interactive information complexity of functions. Let f(x,y) be a function, and suppose Alice is given x and Bob is given y. Informally, the interactive information complexity IC(f) of f is the least amount of information Alice and Bob need to reveal to each other to compute f. Previously, information complexity has been defined with respect to a prior distribution on the input pairs (x,y). Our first goal is to give a definition that is independent of the prior distribution. We show that several possible definitions are essentially equivalent.