Recognizing pro-𝖱 closures of regular languages
Jorge Almeida, José Carlos Costa, Marc Zeitoun · Forum Mathematicum · 2022
Abstract Given a regular language L , we effectively construct a unary semigroup that recognizes the topological closure of L in the free unary semigroup relative to the variety of unary semigroups generated by the pseudovariety 𝖱 {\mathsf{R}} of all finite ℛ {\mathcal{R}} -trivial semigroups. In particular, we obtain a new effective solution of the separation problem of regular languages by 𝖱 {\mathsf{R}} -languages.