Comments on Automata in Random Media

In this paper several approaches are presented to the problem of optimizing the design of a finite automaton for the hypothesis testing problem and the related two-armed bandit problem. It is noted that the two-armed bandit formulation is equivalent to a fundamental question raised by Tsetlin and his colleagues concerning the unknown optimal design of automata in random media. A solution of this problem is given by appropriate application of other work which is presented in condensed and unified form here. Closely related problems involving Markov switching hypotheses and multiple hypotheses remain unsolved.