Bounded-depth circuits: separating wires from gates

We develop a new method to analyze the flow of communication in constant-depth circuits. This point of view allows usto prove new lower bounds on the number of wires required to recognize certain languages. We are able to provide explicit languages that can be recognized by <i>AC</i>⁰ circuits with <i>O</i>(<i>n</i>) gates but not with <i>O</i>(<i>n</i>) wires, and similarly for <i>ACC</i>⁰ circuits. We are also able to characterize exactly the regular languages that can be recognized with <i>O</i>(<i>n</i>) wires, both in <i>AC</i>⁰ and <i>ACC</i>⁰ framework.