Constructions effectives sur les séries formelles d'arbres

Abstract

In this paper we exhibit two different effective constructions of the syntactic algebra U s associated with a recognizable tree series S. In order to make the first construction we only need a natural number n satisfying dim U s⩽n . The second way to obtain U s is by minimization of a given realization of S. We finally describe (effectively) a minimal matrix representation of S.