Universal Theory of Automata, 1

Our purpose in writing this book is to present a universal theory of automata which on one hand unifies the theories of several well-known types of automata and on the other hand allows interesting new applications and results. The frame work for our development is category theory, especially universal constructions in monoidal categories. But we will carefully motivate and introduce all those (and only those) notions and results of category theory which are needed in our approach. The reader is only assumed to be familiar with sets, deterministic functions, relations and the basic no tions of structural mathematics. However, some knowledge of discrete probability distributions, linear algebra and general topology would be useful in understanding the corre sponding applications and in having a better background for the general theory. All our constructions and results are motivated and interpreted carefully with respect to the classical theory of deterministic, partial, linear, topolog ical, nondeterministic, relational and stochastic automata. The book is mainly devoted to students of theoretical com puter science or mathematics and can be used as a textbook in graduate courses or seminars. On the other hand it will also be useful for many other people, who are concerned with the interesting new research area of category theory applied to computation and control.