One-Way Communication Complexity of Computing a Collection of Rational Functions

Abstract

We consider the problem of evaluating a collection of rational functions ƒ 1( x, y), ƒ 2( x, y), . , ƒ s ( x, y) (x ∈ R m , y ∈ R n ) using two processors P 1 and P 2, assuming that processor P 1 (respectively P 2) has access to input x (respectively y) and the functional form of ƒ. We establish, by way of algebraic field extension theory, an almost optimal lower bound on the one-way communication complexity (i.e.. the minimum number of real-valued messages that have to be exchanged). Our result strengthens the early result of Abelson in several directions.