On Deciding Topological Classes of Deterministic Tree Languages (original) (raw)

It has been proved by Niwiński and Walukiewicz that a deterministic tree language is either Π 1 1-complete or it is on the level Π 0 3 of the Borel hierarchy, and that it can be decided effectively which of the two takes place. In this paper we show how to decide if the language recognized by a given deterministic tree automaton is on the Π 0 2 , the Σ 0 2 , or the Σ 0 3 level. Together with the previous results it gives a procedure calculating the exact position of a deterministic tree language in the topological hierarchy.