Une Relation d'Equivalence Decidable sur la Classe des Forêts Reconnaissables

We define, on the class of recognizable sets of trees, a relation ↔ byF1↔F2 if and only ifF1 andF2 are the images by two linear, complete and strict tree-homomorphisms of the same recognizable set of trees. We show that this relation is an equivalence relation and that it is decidable for any pair of recognizable sets whetherF1↔F2.