Multiple Hypothesis Testing by Finite Memory Algorithms

Abstract

In recent years, a theory has been emerging concerning the statistical power of small computers. In the present paper it is proven that in the sense peculiar to this literature, small computers (mathematically equivalent to finite automata) can in general be designed to solve multiple simple hypothesis testing problems. In many cases, only one state for each hypothesis is needed. In a more conventional sense, we reveal the construction of finite automata which implement sequential decision procedures having the capacity to distinguish between any given finite set of probabilities with any desired accuracy. Finally, some results on the ability of finite automata to track time--changing hypotheses are outlined.