GENERAL VARIETIES OF TREE-LANGUAGES

We consider varieties of tree languages which are not restricted to a fixed ranked alphabet, varieties of finite algebras that contain algeb ras of all finite types, and a matching notion of varieties of congrue nces. A variety theorem that yields isomorphisms between the lattices formed by these three types of varieties is proved. To achieve this, s ome basic universal algebra is suitably generalized and we define synt actic algebras so that two tree languages over any alphabets belong to the same varieties exactly in case their syntactic algebras are isomo rphic. Many families of regular tree languages are shown to be varieti es in our sense. In particular, we prove that every family of regular tree languages which can be characterized by syntactic monoids is such a variety, but that the converse does not hold. (C) 1998-Elsevier Sci ence B.V. All rights reserved.