Constraint-generating dependencies

  • Marianne Baudinet
  • Jan Chomicki
  • Pierre Wolper
Contributed Papers Constraints and Dependencies
Part of the Lecture Notes in Computer Science book series (LNCS, volume 893)


Traditionally, dependency theory has been developed for uninterpreted data. Specifically, the only assumption that is made about the data domains is that data values can be compared for equality. However, data is often interpreted and there can be advantages in considering it as such, for instance obtaining more compact representations as done in constraint databases. This paper considers dependency theory in the context of interpreted data. Specifically, it studies constraint-generating dependencies. These are a generalization of equality-generating dependencies where equality requirements are replaced by constraints on an interpreted domain. The main technical results in the paper are a general decision procedure for the implication and consistency problems for constraint-generating dependencies, and complexity results for specific classes of such dependencies over given domains. The decision procedure proceeds by reducing the dependency problem to a decision problem for the constraint theory of interest, and is applicable as soon as the underlying constraint theory is decidable. The complexity results are, in some cases, directly lifted from the constraint theory; in other cases, optimal complexity bounds are obtained by taking into account the specific form of the constraint decision problem obtained by reducing the dependency implication problem.


Integrity Constraint Dependency Theory Constraint Language Quantifier Elimination Quantify Boolean Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    B. Aspvall, M. Plass, and R. Tarjan. A linear-time algorithm for testing the truth of certain quantified boolean formulas. Inf. Process. Lett., 8(3):121–123, 1979.Google Scholar
  2. 2.
    M. Baudinet. On the expressiveness of temporal logic programming. To appear in Information and Computation.Google Scholar
  3. 3.
    M. Baudinet. Temporal logic programming is complete and expressive. In Sixteenth ACM Symposium on Principles of Programming Languages, pages 267–280, Austin, Texas, Jan. 1989.Google Scholar
  4. 4.
    M. Baudinet, J. Chomicki, and P. Wolper. Temporal deductive databases. In A. Tansel, et al., editors, Temporal Databases. Theory, Design, and Implementation, chapter 13, pages 294–320. Benjamin/Cummings, 1993.Google Scholar
  5. 5.
    M. Baudinet, M. Niézette, and P. Wolper. On the representation of infinite temporal data and queries. In Tenth ACM Symposium on Principles of Database Systems, pages 280–290, Denver, Colorado, May 1991.Google Scholar
  6. 6.
    C. Beeri and M. Vardi. A proof procedure for data dependencies. Journal of the ACM, 31(4):718–741, Oct. 1984.Google Scholar
  7. 7.
    A. Brodsky, J. Jaffar, and M. J. Maher. Toward practical constraint databases. In 19th International Conference on Very Large Data Bases, Dublin, Aug. 1993.Google Scholar
  8. 8.
    A. Brodsky, C. Lassez, and J.-L. Lassez. Separability of polyhedra and a new approach to spatial storage. In Proceedings of the First Workhop on Principles and Practice of Constraint Programming, Newport, Rhode Island, Apr. 1993.Google Scholar
  9. 9.
    J. Chomicki. Polynomial time query processing in temporal deductive databases. In Ninth ACM Symposium on Principles of Database Systems, pages 379–391, Nashville, Tennessee, Apr. 1990.Google Scholar
  10. 10.
    J. Chomicki and T. Imieliński. Temporal deductive databases and infinite objects. In Seventh ACM Symposium on Principles of Database Systems, pages 61–73, Austin, Texas, Mar. 1988.Google Scholar
  11. 11.
    J. Chomicki and T. Imieliński. Finite Representation of Infinite Query Answers. ACM Transactions on Database Systems, 18(2):181–223, June 1993.Google Scholar
  12. 12.
    J. Cox and K. McAloon. Decision procedures for constraint based extensions of Datalog. In F. Benhamou and A. Colmerauer, editors, Constraint Logic Programming: Selected Research. MIT Press, 1993.Google Scholar
  13. 13.
    M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York, 1979.Google Scholar
  14. 14.
    S. Ginsburg and R. Hull. Order dependency in the relational model. Theoretical Computer Science, 26:149–195, 1983.Google Scholar
  15. 15.
    S. Ginsburg and R. Hull. Sort sets in the relational model. Journal of the ACM, 33(3):465–488, July 1986.Google Scholar
  16. 16.
    A. Gupta, Y. Sagiv, J. D. Ullman, and J. Widom. Constraint checking with partial information. In Thirteenth ACM Symposium on Principles of Database Systems, pages 45–55, Minneapolis, MN, May 1994.Google Scholar
  17. 17.
    N. S. Ishakbeyoğlu and Z. M. Ozsoyoğlu. On the maintenance of implication integrity constraints. In Fourth International Conference on Database and Expert Systems Applications, pages 221–232, Prague, Sept. 1993. LNCS 720, Springer.Google Scholar
  18. 18.
    C. Jensen and R. Snodgrass. Temporal specialization. In Eighth International Conference on Data Enfineering, pages 594–603, Tempe, Arizona, Feb. 1992. IEEE.Google Scholar
  19. 19.
    F. Kabanza, J.-M. Stévenne, and P. Wolper. Handling infinite temporal data. In Ninth ACM Symposium on Principles of Database Systems, pages 392–403, Nashville, Tennessee, Apr. 1990.Google Scholar
  20. 20.
    P. Kanellakis. Elements of relational database theory. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B, chapter 17, pages 1073–1158. Elsevier/MIT Press, 1990.Google Scholar
  21. 21.
    P. C. Kanellakis, G. M. Kuper, and P. Revesz. Constraint query languages. In Ninth ACM Symposium on Principles of Database Systems, pages 299–313, Nashville, Tennessee, Apr. 1990.Google Scholar
  22. 22.
    P. C. Kanellakis, S. Ramaswamy, D. E. Vengroff, and J. S. Vitter. Indexing for data models with constraints and classes. In Twelfth ACM Symposium on Principles of Database Systems, pages 233–243, Washington, DC, May 1993.Google Scholar
  23. 23.
    M. Koubarakis. Representation and querying in temporal databases: the power of temporal constraints. In Ninth International Conference on Data Engineering, Vienna, Austria, Apr. 1993.Google Scholar
  24. 24.
    D. Maier. The Theory of Relational Databases. Computer Science Press, 1983.Google Scholar
  25. 25.
    P. Revesz. A closed form for Datalog queries with integer order. In S. Abiteboul and P. Kanellakis, editors, ICDT '90, Proceedings of the Third International Conference on Database Theory, pages 187–201, Paris, Dec. 1990. LNCS 470, Springer.Google Scholar
  26. 26.
    D. Rosenkrantz and H. B. I. Hunt. Processing conjunctive predicates and queries. In International Conference on Very Large Data Bases, pages 64–72, 1980.Google Scholar
  27. 27.
    A. Schrijver. Theory of Linear and Integer Programming. John Wiley & Sons, 1986.Google Scholar
  28. 28.
    D. Srivastava. Subsumption in constraint query languages with linear arithmetic constraints. In Second International Symposium on Artificial Intelligence and Mathematics, Fort Lauderdale, Florida, Jan. 1992.Google Scholar
  29. 29.
    B. Thalheim. Dependencies in Relational Databases. Teubner-Texte zur Mathematik, Band 126. B.G. Teubner Verlagsgesellschaft, Stuttgart, 1991.Google Scholar
  30. 30.
    J. D. Ullman. Principles of Database and Knowledge-Base Systems — Volume II: The New Technologies. Computer Science Press, 1989.Google Scholar
  31. 31.
    R. van der Meyden. The complexity of querying indefinite data about linearly ordered domains. In Eleventh ACM Symposium on Principles of Database Systems, pages 331–345, San Diego, California, June 1992.Google Scholar
  32. 32.
    M. Vardi. Fundamentals of dependency theory. In E. Börger, editor, Trends in Theoretical Computer Science, pages 171–224. Computer Science Press, 1988.Google Scholar
  33. 33.
    X. Zhang and Z. M. Ozsoyoğlu. On efficient reasoning with implication constraints. In Third International Conference on Deductive and Object-Oriented Databases, Phoenix, Arizona, Dec. 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Marianne Baudinet
    • 1
  • Jan Chomicki
    • 2
  • Pierre Wolper
    • 3
  1. 1.InformatiqueUniversité Libre de BruxellesBrusselsBelgium
  2. 2.Dept of Computing and Information SciencesKansas State UniversityManhattanUSA
  3. 3.Institut MontefioreUniversité de LiègeLiège Sart-TilmanBelgium

Personalised recommendations