  We study the class of quasi-alphabetic relations, i.e., tree transformations
defined by tree bimorphisms with two quasi-alphabetic tree homomorphisms and a
regular tree language. We present a canonical representation of these
relations; as an immediate consequence, we get the closure under union. Also,
we show that they are not closed under intersection and complement, and do not
preserve most common operations on trees (branches, subtrees, v-product,
v-quotient, f-top-catenation). Moreover, we prove that the translations defined
by quasi-alphabetic tree bimorphism are exactly products of context-free string
languages. We conclude by presenting the connections between quasi-alphabetic
relations, alphabetic relations and classes of tree transformations defined by
several types of top-down tree transducers. Furthermore, we get that
quasi-alphabetic relations preserve the recognizable and algebraic tree
languages.
