Finite memory multiple hypothesis testing: Close-to-optimal schemes for Bernoulli problems

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.