ON THE COMPLEXITY OF RECOGNIZABLE ω-TREE SETS AND NERODE THEOREM

In this paper we consider the extension of Nerode theorem to infinite trees. Unfortunately, we prove that this extension is not possible. We give some characterizations of recognizable and rational ω-tree sets in terms of ω-tree automata. We consider some complexity measures of recognizable and rational ω-tree sets and prove that these measures define infinite hierarchies.