Machines in a Category: An Expository Introduction
Michael A. Arbib, Ernest G. Manes · SIAM Review · 1974
We present for the first time a general definition of machines in an arbitrary category which unifies the theories of sequential machines, linear control systems, tree automata and stochastic automata. To make the paper relatively accessible, we provide a careful exposition of the notions of automata theory we seek to unify, of some basic results of automata theory we seek to generalize, and of elementary concepts we require from category theory. We then state and prove our new fundamental realization theorem which shows how to construct a broad variety of machines with prescribed behavior.