Automata that Distinguish Random Media

The interrelationship of the asymptotic optimality of a sequence of automata and aggregates of automata is investigated. It is proved that asymptotically optimal sequences of automata can generate both asymptotically optimal and poorly behaved sequences of aggregates on one and the same set of media for an aggregate. The proof is based on the fact that a statistic distinguishing random media corresponds to a sequence of automata that asymptotically distinguishes those media.