Categories of fuzzy-type automata with Kleisli morphisms

Abstract

We introduce the categories of monadic automata, where morphisms between automata are relations defined by monads, that is, morphisms in the Kleisli categories. We show that many standard categories of automata including deterministic, non-deterministic, or fuzzy automata with relations as morphisms are special examples of this category. We also show that there is a strong relation among functors between the Kleisli categories, on the one hand, and functors between these categories of monadic automata, on the other. We extend the definition of a language accepted by a monadic automata with Kleisli morphisms and investigate relationships between categories of these languages and Kleisli categories.