Effective construction of the syntactic algebra of a recognizable series on trees

Abstract

In this paper we exhibit two different effective constructions of the syntactic algebraA S associated to a recognizable formal series on treesS. The one method consists of a direct construction of (=a copy ofA S ) which is the subspace with the natural algebra structure. We first determine a basis of the subspace and then, using the junction isomorphism we obtain a basis for . The second method consists of considering an arbitrary surjective realization (A, φ) ofS, defining an appropriate ideal ℬ ofA and then constructing the quotient algebraA/ℬ this quotient is isomorphic toA S and thus independent of the choice of (A S φ).