MPI-I-1999-2-001

We introduce a new class of finite automata. They are usual bottom-up tree automata that run on DAG representations of finite trees. We prove that the emptiness problem for this class of automata is NP-complete. Using these automata we prove the decidability of directional type checking for logic programs, and thus we improve earlier results by Aiken and Lakshman. We also show an application of these automata in solving systems of set constraints, which gives a new view on the satisfiability problem for set constraints with negative constraints.