Simultaneous Messages vs. Communication

In the multiparty communication game introduced by Chandra, Furst, and Lipton CFL] (1983), k players wish to evaluate collaboratively a function f (x0; : : : ; xk?1) for which player i sees all inputs except xi: The players have unlimited computational power. The objective is to minimize the amount of communication. We consider a restricted version of the multiparty communication game which we call the simultaneous messages model. The diierence is that in this model, each of the k players simultaneously sends a message to a referee, who sees none of the input. The referee then announces the function value. We demonstrate an exponential gap between the Simultaneous Messages and the Communication models for up to (log n) 1? players, for any > 0: The separation is obtained by comparing the respective complexities of the generalized addressing function, GAFG;k, in each model. In addition, we give a nontrivial protocol for GAFG;k for G = Z t 2 ; which is very eecient when the number of players is 2 + log n. We also examine a diierent class of functions which have very eecient protocols for k 2 + log n players. to separate ACC from complexity classes containing it.