Automata Minimization: a Functorial Approach

Abstract

In this paper we regard languages and their acceptors - such as deterministicor weighted automata, transducers, or monoids - as functors from inputcategories that specify the type of the languages and of the machines tocategories that specify the type of outputs. Our results are as follows: A) We provide sufficient conditions on the output category so thatminimization of the corresponding automata is guaranteed. B) We show how to lift adjunctions between the categories for output valuesto adjunctions between categories of automata. C) We show how this framework can be instantiated to unify several phenomenain automata theory, starting with determinization, minimization and syntacticalgebras. We provide explanations of Choffrut's minimization algorithm forsubsequential transducers and of Brzozowski's minimization algorithm in thissetting.Comment: journal version of the CALCO 2017 paper arXiv:1711.0306