On tests with finite memory in finite time (Corresp.)

The purpose of this correspondence is to display an inductive proof of an optimality result for testing symmetric simple hypotheses concerning a binomial parameter with a three-state memory and observations. Specifically, it is shown that if one restricts attention to three-state automata allowing transitions only between adjacent states, then no artificial randomization is required in the middle state of the optimal machine. The success in this problem of what will be called simultaneous induction suggests the possibility of obtaining characterizations of optimal automata in more general problems by similar techniques.