EFFICIENT STATE-SPLITTING M. A. Arbib Department of Computer and Information Science University of Massachusetts at Amherst Amherst, Massachusetts 01002 USA E. G. Manes Department of Mathematics and Statistics University of Massachusetts at Amherst Amherst, Massachusetts 01002 USA There are many 'storage problems' in computer science which take the form: find a small subfamily of objects which can be used to generate a given larger family. A particular such problem is that of realizing a response function f : X" ~ Y by an automaton which, in one of a number of possible senses, allows fstate-splitting' and so has fewer states than the minimal deterministic realization. A precise statement appears in section 2. As a prototype example, consider the 1-input automaton with split initial state and n+m states shown below: If m and n are relatively prime, the minimal deterministic realization has mn states. In this preliminary report we consider specializations of our theory of fuzzy automata CI] [2] . The first two sections provide a general discussion of automata with distribution states. The discussion is brief since proofs and further discussion can be found in CIJ and [3J . In the remainder of the paper we pose a The authors gratefully acknowledge support from the National Science Foundation under grants DCR72-03753 A01 and MCS76-84477.