Homomorphic representations by products of tree automata

Abstract

In this paper we give necessary and sufficient conditions for sets of frontier-to-root tree automata to be homomorphically complete. Moreover, it is shown that-in contrast to the classical case-a homomorphically complete set not necessarily contains a one-element homomorphically complete subset. Similar results can be found in [6] for root-to-frontier (ascending) tree automata.

The results of this paper were obtained between September 1, 1992 and February 28, 1993 when the author, as a Research Professor of the Academy of Finland, worked with Arto Salomaa in Turku. The research was partially supported by the Hungarian National Foundation for Scientific Research Grant 2035.