Abstract
The design of optimal, time-invariant, randomized, finite-state automata for K -hypothesis testing is an open problem for K > 2 . A lower bound is constructed on the smallest probability of error achievable by m -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.
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