Worst-case interactive communication. I. Two messages are almost optimal

The reduction in communication achievable by interaction is investigated. The model assumes two communicators: an informant having a random variable X, and a recipient having a possibly dependent random variable Y. Both communicators want the recipient to learn X with no probability of error, whereas the informant may or may not learn Y. To that end, they alternate in transmitting messages comprising finite sequences of bits. Messages are transmitted over an error-free channel and are determined by an agreed-upon, deterministic protocol for (X,Y) (i.e. a protocol for transmitting X to a person who knows Y). A two-message protocol is described, and its worst case performance is investigated