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

Abstract We consider the problem of evaluating a collection of rational functions ƒ1(x, y), ƒ2(x, y), . . . , ƒs(x, y) (x ∈ R m, y ∈ R n) using two processors P1 and P2, assuming that processor P1 (respectively P2) 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.