Lower Bounds on the Randomized Communication Complexity of Read-Once Functions

Abstract. We prove lower bounds on the randomized two-party communication complexity of functions that arise from read-once boolean formulae. A read-once boolean formula is a formula in propositional logic with the property that every variable appears exactly once. Such a formula can be represented by a tree, where the leaves correspond to variables, and the internal nodes are labeled by binary connectives. Under certain assumptions, this representation is unique. Thus, one can define the depth of a formula as the depth of the tree that represents it. The complexity of the evaluation of general read-once formulae has attracted interest mainly in the decision tree model. In the communication complexity model many interesting results deal with specific read-once formulae, such as DISJOINTNESS and TRIBES. In this paper we use information theory methods to prove lower bounds that hold for any read-once formula. Our lower bounds are of the form n(f)/cd(f), where n(f) is the number of variab...

• Type: Journal
• Year: 2010
• Where: CC
• Authors: Nikos Leonardos, Michael Saks
• Keywords: CC 2010, Communication Complexity, Lower Bounds, Read-once Formulae, System Software