Cost functors and optimal realization

摘要

We provide a general theory of optimal realization, generalizing the minimal realization construction of automata theory. We use a categorical framework to capture general classes of deterministic and nondeterministic realization problems. We define cost functors over a category of systems relative to which optimal realizations are defined. Finally, in order to approach the generalized minimal realization problem of nondeterministic automata, we propose a quotient category of these automata which fulfills the generalized minimal realization principle.