Unified Representation of Automata

Abstract

Starting with the examples of deterministic, nondeterministic, stochastic, linear, bilinear and topological automata it will be shown that the notion of automata in monoidal categories provides an appropriate general setting to get a unified representation of all these different kinds of automata. Moreover partial, relational and relational topological automata are given as examples and several other types will be mentioned in the following chapters. For each special type we give references to the literature. The idea of studying automata in monoidal categories is due to L. Budach and H.-J. Hoehnke in [17] and J. A. Goguen in [44,45]. We start with the definition and automata theoretic interpretation of automata in the sense of G. H. M e a 1 y. The notions of Moore- and Medvedev-automata will be given at the end of the chapter.