A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
Using descriptions of trees in a tree adjoining grammar
Computational Linguistics
Studies in the logic of trees with applications to grammar formalisms
Studies in the logic of trees with applications to grammar formalisms
Sequential Construction of Logical Forms
LACL '98 Selected papers from the Third International Conference, on Logical Aspects of Computational Linguistics
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Constraints over Lambda-Structures in semantic underspecification
COLING '98 Proceedings of the 17th international conference on Computational linguistics - Volume 1
D-theory: talking about talking about trees
ACL '83 Proceedings of the 21st annual meeting on Association for Computational Linguistics
Reasoning with descriptions of trees
ACL '92 Proceedings of the 30th annual meeting on Association for Computational Linguistics
Dominance Constraints in Context Unification
LACL '98 Selected papers from the Third International Conference, on Logical Aspects of Computational Linguistics
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Context Unification and Traversal Equations
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Dominance Constraints with Set Operators
CL '00 Proceedings of the First International Conference on Computational Logic
Parallelism and Tree Regular Constraints
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Well-nested parallelism constraints for ellipsis resolution
EACL '03 Proceedings of the tenth conference on European chapter of the Association for Computational Linguistics - Volume 1
On testing satisfiability of tree pattern queries
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
Stratified context unification is NP-complete
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
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Dominance constraints for finite tree structures are widely used in several areas of computational linguistics including syntax, semantics, and discourse. In this paper, we investigate algorithmic and complexity questions for dominance constraints and their first-order theory. The main result of this paper is that the satisfiability problem of dominance constraints is NP-complete. We present two NP algorithms for solving dominance constraints, which have been implemented in the concurrent constraint programming language Oz. Despite the intractability result, the more sophisticated of our algorithms performs well in an application to scope underspecification. We also show that the positive existential fragment of the first-order theory of dominance constraints is NP-complete and that the full first-order theory has non-elementary complexity.