On Quasi-Products of Tree Automata

In this paper we introduce the concept of the quasi-product of tree automata. In a quasi-product the inputs of the component tree automata are operational symbols in which permutation and unification of variables are allowed. It is shown that in sets of tree automata which are homomorphically complete with respect to the quasiproduct the essentially unary operations play the basic role among all operations with nonzero ranks. Furthermore, we give a characterization of homomorphically complete sets which is similar to the classical one.