Automata Minimization: a Functorial Approach

In this paper we regard languages and their acceptors – such as deterministic or weighted automata, transducers, or monoids – as functors from input categories that specify the type of the languages and of the machines to categories that specify the type of outputs. Our results are as follows: a) We provide sufficient conditions on the output category so that minimization of the corresponding automata is guaranteed. b) We show how to lift adjunctions between the categories for output values to adjunctions between categories of automata. c) We show how this framework can be instantiated to unify several phenomena in automata theory, starting with determinization and minimization (which have been previously studied from a coalgebraic and duality theoretic perspective). We also show how subsequential transducers can be seen as functors valued in a Kleisli category and explain Choffrut’s minimization algorithm. 1998 ACM Subject Classification F.1.1