Discrete-time machines in closed monoidal categories. I

This paper develops a minimal realization theory for discrete-time machines with structure in a suitable closed monoidal category. By specifying the category a number of applications arise, most of them new. Minimal realization is stated as an adjunction between an input-output behavior functor and a realization functor. The very existence of an adjunction yields several new structural results on minimal realization. As preliminaries, certain aspects of categorical algebra are reviewed, and a theory of discrete-time transition systems is developed. The concept of an X-module and an initial object theorem are especially important. A number of examples of suitable categories is given, but discussion of the resulting machine theories is deferred to a subsequent paper