The disjointness problem is one of the most important questions in communication complexity, and lower bounds for disjointness have been used to derive lower bounds for streaming algorithms, data structures, barriers in complexity (algebraization), approaches for circuit lower bounds, proof complexity, game theory. Some sources on this include the survey “The Story of Set Disjointness” by Chatt...

The first section starts with the basic definitions following mainly the notations of the book written by E. Kushilevitz and N. Nisan [8]. This whole thesis started from this book and some parts follow the proofs from there but I always tried to simplify and improve them, I even discovered and corrected a false claim. But most of the results are mine, supervised by Zoltán Király. At the beginni...

In this chapter we survey the theory of two-party communication complexity. This field of theoretical computer science aims at studying the following, seemingly very simple, scenario: There are two players Alice who holds an n-bit string x and Bob who holds an n-bit string y. Their goal is to communicate in order to compute the value of some boolean function f(x, y), while exchanging a number o...