Visibly pushdown automata on trees: universality and u-universality
  An automaton is universal if it accepts every possible input. We study the notion of u-universality, which asserts that the automaton accepts every input starting with u. Universality and u-universality are both EXPTIME-hard for non-deterministic tree automata. We propose efficient antichain-based techniques to address these problems for visibly pushdown automata operating on trees. One of our approaches yields algorithms for the universality and u-universality of hedge automata. 
V\'eronique Bruy\`ere, Marc Ducobu, Olivier Gauwin
cs.FL