Publications in Communication Complexity Theory

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 for Logspace, and more. Many more applications were found later in a variety of contexts, including circuit complexity and the analysis of streaming data; the results and techniques continue to inspire work to this date. The paper introduced “cylinder intersections” and characterized NOF complexity in terms of these. It introduced an iterated Cauchy-Schwarz scheme to prove lower bounds on the discrepancy of certain functions over cyclinder-intersections. This method has found many subsequent applications and is similar to a method used by Bourgain two decades later to estimate certain exponential sums (C. R. Math. 2005).