The effects of randomization on finite memory decision schemes

This paper is concerned with the effects of randomization on finite memory decision rules [1]. It is shown that for any twohypothesis testing problem, there exists a b < ??, such that for all B, the optimal randomized rule using a memory with B bits has a probability of error no smaller than that of the optimal deterministic rule using B+b bits. Thus as B???? the fraction of bits lost by using deterministic rules tends to zero, and in this sense deterministic rules are asymptotically optimal.