Dominance Constraints: Algorithms and Complexity

  • Alexander Koller
  • Joachim Niehren
  • Ralf Treinen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2014)


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.


Dominance constraints complexity computational linguistics underspecification constraint programming 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Alexander Koller
    • 1
  • Joachim Niehren
    • 2
  • Ralf Treinen
    • 3
  1. 1.Department of Computational LinguisticsUniversität des SaarlandesSaarbrückenGermany
  2. 2.Programming Systems LabUniversität des SaarlandesSaarbrückenGermany
  3. 3.Laboratoire de Recherche en InformatiqueUniversité Paris-SudOrsayFrance

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