Abstract
A complete non-deterministic automaton may be viewed as a relational system with unary and binary relations. These relations must satisfy certain closure properties. On the basis of these properties, recent results concerning the representation of general relational systems as direct and subdirect products are specialized to more precise results for non-deterministic automata. For example, we prove that the representations of a non-deterministic automaton as a direct product correspond in a one-to-one way to certain families ofideals of the automaton. The ideal of an automaton are seen to play an essential role in describing its structure, and a number of the properties of ideals are delineated.
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