The EQUALITY problem---where Alice and Bob must decide if their respective
inputs are equal---is usually one's first encounter with communication
complexity. Its deterministic and randoemized complexity were settled decades
ago, but we find several new things to say by considering two subtle aspects.
First, we study the expected communication cost (at a worst-case input) for a
protocol that uses limited interaction. Second, we study the information cost of
such protocols. We obtain asymptotically optimal rounds-versus-communication and
rounds-versus-information tradeoffs for EQUALITY.

As an application of our information cost bounds, we obtain new, and
asymptotically optimal, bounded-round randomized lower bounds for OR-EQUALITY
and k-DISJOINTNESS (where input sets have size <= k).