 -hypothesis testing is an open problem for
 -hypothesis testing is an open problem for  . A lower bound is constructed on the smallest probability of error achievable by
 . A lower bound is constructed on the smallest probability of error achievable by  -state automata solving a three-hypothesis Bernoulli problem. A class of close-to-optimal automata is exhibited that requires at most one extra bit of memory to match the performnnce of an optimal automaton.
 -state automata solving a three-hypothesis Bernoulli problem. A class of close-to-optimal automata is exhibited that requires at most one extra bit of memory to match the performnnce of an optimal automaton.