The curse of the Revelation Principle is that it leads us to focus on unrealistic mechanisms in which agents report all private information to the principal, who then makes all decisions centrally. This is not true when communication costs are introduced. Then partial communication of information, sequential back-and-forth conversations, and decentralization of decisions become part of optimal ...

We study problems in randomized communication complexity when the protocol is only required to attain some small advantage over purely random guessing, i.e., it produces the correct output with probability at least ǫ greater than one over the codomain size of the function. Previously, Braverman and Moitra (STOC 2013) showed that the set-intersection function requires Θ(ǫn) communication to achi...

In two-party quantum communication complexity, Alice and Bob receive some classical inputs and wish to compute some function that depends on both these inputs, while minimizing the communication. This model has found numerous applications in many areas of computer science. One question that has received a lot of attention recently is whether it is possible to perform such protocols in a private...

This lecture focuses on proving communication lower bounds using matrix rank. Similar to fooling sets and rectangle size bounds, the matrix rank technique also gives a lower bound on the number of monochromatic rectangles in any partition of X × Y but it does so in an algebraic way[1]. This makes algebraic tools available for proving communication lower bounds. We begin by solving the problem a...

We consider a variation of the multi-party communication complexity scenario where the parties are supplied with an extra resource: particles in an entangled quantum state. We show that, although a prior quantum entanglement cannot be used to simulate a communication channel, it can reduce the communication complexity of functions in some cases. Specifically, we show that, for a particular func...

Quantum computing combines the framework of quantum mechanics with that of computer science. In this paper we give a short introduction to quantum computing and survey the results in the area of quantum communication complexity.

This pair of papers contains lower bounds in the “number-on-forehead” (NOF) model of multi-party communication complexity that remain the strongest even to date, after 24 years, in spite of considerable effort. The paper includes applications to a variety of models of computation: time-space tradeoff for multi-head Turing machines, lower bounds for branching programs, pseudorandom generators fo...

The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on communication complexity theory and, as a by-product, we provide (yet another) classification of cellular automata.

The model consists of two parties [Yao79], Alice and Bob, holding inputs x ∈ X and y ∈ Y respectively. They exchange messages in order to compute a function f : X×Y → {0, 1} at (x, y); their goal is to do this with minimal amount of interaction, which is some measure of the communication between the two parties and will usually be the total number of bits exchanged by the parties. Figure 1 illu...