  We study cellular automata with respect to a new communication complexity
problem: each of two players know half of some finite word, and must be able to
tell whether the state of the central cell will follow a given evolution, by
communicating as little as possible between each other. We present some links
with classical dynamical concepts, especially equicontinuity, expansiveness,
entropy and give the asymptotic communication complexity of most elementary
cellular automata.
