Tree Automata with Global Constraints for Infinite Trees

We study an extension of tree automata on infinite trees with global equality and disequality constraints. These constraints can enforce that all subtrees for which in the accepting run a state q is reached (at the root of that subtree) are identical, or that these trees differ from the subtrees at which a state q' is reached. We consider the closure properties of this model and its decision problems. While the emptiness problem for the general model remains open, we show the decidability of the emptiness problem for the case that the given automaton only uses equality constraints.