The emptiness problem for tree automata with at least one global disequality constraint is NP-hard

•Tree Automata with constraints are a relevant for modeling programs, protocols and XML-like documents.•The Emptiness problem for TAG∧ is decidable but the only known algorithm is non elementary.•Studying the complexity of sub-classes of TAG∧ is therefore a challenging problem.•We prove that the emptiness problem for TAG∧ with at least one disequality constraint is NP-hard.

The model of tree automata with global equality and disequality constraints was introduced in 2007 by Filiot, Talbot and Tison, and extended in various ways since then. In this paper we show that if there is at least one disequality constraint, the emptiness problem is NP-hard.