Theory of Computing Systems

, Volume 42, Issue 2, pp 239–255 | Cite as

Complexity of Clausal Constraints Over Chains

  • Nadia Creignou
  • Miki HermannEmail author
  • Andrei Krokhin
  • Gernot Salzer


We investigate the complexity of the satisfiability problem of constraints over finite totally ordered domains. In our context, a clausal constraint is a disjunction of inequalities of the form xd and xd. We classify the complexity of constraints based on clausal patterns. A pattern abstracts away from variables and contains only information about the domain elements and the type of inequalities occurring in a constraint. Every finite set of patterns gives rise to a (clausal) constraint satisfaction problem in which all constraints in instances must have an allowed pattern. We prove that every such problem is either polynomially decidable or NP-complete, and give a polynomial-time algorithm for recognizing the tractable cases. Some of these tractable cases are new and have not been previously identified in the literature.


Constraint satisfaction problems Complexity Finite totally ordered domains Inequalities Clausal patterns Dichotomy theorem 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Nadia Creignou
    • 1
  • Miki Hermann
    • 2
    Email author
  • Andrei Krokhin
    • 3
  • Gernot Salzer
    • 4
  1. 1.LIF (CNRS, UMR 6166)Univ. de la MéditerranéeMarseille cedex 9France
  2. 2.LIX (CNRS, UMR 7161)École PolytechniquePalaiseau cedexFrance
  3. 3.Department of Computer ScienceUniversity of DurhamDurhamUK
  4. 4.Technische Universität WienViennaAustria

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