Reasoning About Co-Büchi Tree Automata

We consider co–Büchi tree automata along with both alternating and generalized paradigms, as a characterization of the class of languages whose complement is accepted by generalized Büchi tree automata. We first prove that for alternating generalized co–Büchi tree automata the simulation theorem does not hold and the generalized acceptance does not add to the expressive power of the model. Then, we show that the emptiness problem for this class is Exptime-complete. For the class of languages whose complement is accepted by deterministic generalized Büchi tree automata, we get better complexity bounds: we give a characterization of this class in terms of generalized co–Büchi tree automata that yields an algorithm for checking the emptiness that takes time linear in the product of the number of states and the number of sets in the acceptance condition. Finally, we compare the classes of languages whose complement is respectively accepted by deterministic and nondeterministic Büchi tree automata with the main classes studied in the literature.