Alphabetic Tree Relations

Abstract We study the class of tree transductions induced by bimorphisms (ϕ, R , ϕ′) with ϕ,ϕ′ alphabetic homomorphisms and R a recognizable forest; this class contains many of classical tree-transformations such as union and intersection with a recognizable forest, a -product, a -quotient, top-catenation, branches, subtrees, initial and terminal subtrees, largest common initial subtree, etc. Furthermore, the considered transductions are closed under composition and inversion and preserve the recognizable and algebraic forests; by applying the last fact to the classical tree transformations cited above, we obtain a series of remarkable results. We show that Takahashi's relations A ⊆ T Σ × T Γ can be identified with the squeleton-preserving Σ ∇ Γ -recognizable subsets of T Σ × T Γ . Finally, we give a classification of some remarkable subclasses of the class of alphabetic transductions.