Algebraic tools for the concatenation product

Abstract

This paper is a contribution to the algebraic study of the concatenation product. In the first part of the paper, we extend to the ordered case standard algebraic tools related to the concatenation product, like the Schützenberger product and the relational morphisms. We show in a precise way how the ordered Schützenberger product corresponds to polynomial operations on languages. In the second part of the paper, we apply these results to establish a bridge between the three standard concatenation hierarchies, namely the Straubing–Thérien hierarchy, the Brzozowski's (or dot-depth) hierarchy and the group hierarchy.