Random Databases and Threshold for Monotone Non-recursive Datalog

  • Konstantin Korovin
  • Andrei Voronkov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3618)


In this paper we define a model of randomly generated databases and show how one can compute the threshold functions for queries expressible in monotone non-recursive datalog ≠ . We also show that monotone non-recursive datalog ≠  cannot express any property with a sharp threshold. Finally, we show that non-recursive datalog ≠  has a 0–1 law for a large class of probability functions, defined in the paper.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bollobás, B.: Random graphs. In: Combinatorics (Swansea, 1981). London Math. Soc. Lecture Note Ser, vol. 52, pp. 80–102. Cambridge Univ. Press, Cambridge (1981)CrossRefGoogle Scholar
  2. 2.
    Bollobás, B.: Random graphs. Academic Press Inc, London (1985)MATHGoogle Scholar
  3. 3.
    Bollobás, B., Thomason, A.: Threshold functions. Combinatorica 7, 35–38 (1987)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    de Rougemont, M.: The reliability of queries. In: Proceedings of the Fourteenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, San Jose, California, May 22-25, pp. 286–291. ACM Press, New York (1995)CrossRefGoogle Scholar
  5. 5.
    Ebbinghaus, H.-D., Flum, J.: Finite Model Theory. In: Perspectives in Mathematical Logic, Springer, Heidelberg (1999)Google Scholar
  6. 6.
    Erdős, P., Rényi, A.: On the evolution of random graphs. Magyar Tud. Akad. Mat. Kutató Int. Kőzl 5, 17–61 (1960)Google Scholar
  7. 7.
    Fagin, R.: Probabilities on finite models. Journal of Symbolic Logic 41, 50–58 (1976)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Friedgut, E.: Sharp thresholds of graph properties, and the k-sat problem. J. Amer. Math. Soc. 12(4), 1017–1054 (1999)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Glebskii, Y., Kogan, M., Liogonkii, M., Talanov, V.: Range and degree of realizability of formulas in the restricted predicate calculus. Kibernetika 5, 17–27 (1969) (in Russian); English translation in Cybernetics 5, 142–154 (1969)MathSciNetGoogle Scholar
  10. 10.
    Grädel, E., Gurevich, Y., Hirsch, C.: The complexity of query reliability. In: Proceedings of the Seventeenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, Seattle, Washington, June 1-3, pp. 227–234. ACM Press, New York (1998)CrossRefGoogle Scholar
  11. 11.
    Janson, S., Łuczak, T., Ruciński, A.: Random graphs. John Wiley & Sons, Inc, Chichester (2000)MATHGoogle Scholar
  12. 12.
    Korovin, K., Voronkov, A.: Random databases and threshold for monotone non-recursive datalog. Preprint, School of Computer Science, The University of Manchester (2005)Google Scholar
  13. 13.
    Kumar, R., Raghavan, P., Rajagopalan, S., Sivakumar, D., Tomkins, A., Upfal, E.: The web as a graph. In: Proceedings of the Nineteenth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, Dallas, Texas, USA, May 15-17, pp. 1–10. ACM, New York (2000)CrossRefGoogle Scholar
  14. 14.
    Libkin, L.: Elements of Finite Model Theory. In: Texts in Theoretical Computer Science, Springer, Heidelberg (2004)Google Scholar
  15. 15.
    Lifschitz, S., Vianu, V.: A probabilistic view of Datalog parallelization. Theoretical Computer Science 190(2), 211–239 (1998)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Shelah, S., Spencer, J.: Zero one laws for sparse random graphs. Journal of the AMS 1(1), 97–115 (1988)MATHMathSciNetGoogle Scholar
  17. 17.
    Spencer, J.: The Strange Logic of Random Graphs. In: Algorithms and Combinatorics, vol. 22, Springer, Heidelberg (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Konstantin Korovin
    • 1
  • Andrei Voronkov
    • 1
  1. 1.School of Computer ScienceThe University of Manchester 

Personalised recommendations