Functional Dependencies on Extended Relations Defined by Regular Languages

  • Gyula I. Szabó
  • András Benczúr
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7153)


In this paper, we first rephrase the notion of extended tuple as a sentence from a regular language generated by a grammar G where the nonterminal symbols of the grammar are the attribute names of the tuple. Finite sets of extended tuples play the role of extended relation instances. Then we introduce the dual language, which generates the accepted tuple-types of the extended relation. We define the syntactical form of functional dependencies for extended relation on the graph of the finite state automaton associated to the dual language. Using this model we can handle extended relations generated by recursive regular expressions too. The implication problem of our class of dependencies is decidable by a version of Chase algorithm specified on the graph of the associated FSA.


Functional Dependency Regular Expression Integrity Constraint Regular Language State Automaton 
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.
    Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley (1995)Google Scholar
  2. 2.
    Amano, S., Libkin, L., Murlak, F.: XML schema mappings. In: Proceedings of the Twenty-Eighth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, Providence, Rhode Island, USA, June 29-July 01, pp. 33–42 (2009)Google Scholar
  3. 3.
    Arenas, M., Libkin, L.: A normal form for XML documents. ACM TODS 29, 195–232 (2004)CrossRefGoogle Scholar
  4. 4.
    Buneman, P., Davidson, S.B., Fan, W., Hara, C.S., Tan, W.C.: Keys for XML. Computer Networks 39(5), 473–487 (2002)CrossRefzbMATHGoogle Scholar
  5. 5.
    Chen, Y., Davidson, S.B., Zheng, Y.: Constraint Preserving XML Storage in Relations. In: Proceedings of the International Workshop on the Web and Databases (WEBDB), pp. 7–12 (2002)Google Scholar
  6. 6.
    Lee, D., Mani, M., Murata, M.: Reasoning about XML Schema Languages using Formal Language Theory. Technical Report, IBM Almaden Research Center, RJ# 10197, Log# 95071 (2000),
  7. 7.
    Davidson, S., Fan, W., Hara, C.: Propagating XML constraints to relations. Journal of Computer and System Sciences 73(3), 316–361 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Hartmann, S., Köhler, H., Trinh, T.: On the Existence of Armstrong Data Trees for XML Functional Dependencies. In: Link, S., Prade, H. (eds.) FoIKS 2010. LNCS, vol. 5956, pp. 94–113. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Hartmann, S., Link, S.: Efficient reasoning about a robust XML key fragment. ACM Trans. Database Syst. 34(2) (2009)Google Scholar
  10. 10.
    Hartmann, S., Link, S., Trinh, T.: Solving the Implication Problem for XML Functional Dependencies with Properties. In: Dawar, A., de Queiroz, R. (eds.) WoLLIC 2010. LNCS, vol. 6188, pp. 161–175. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Lv, T., Yan, P.: Mapping Relational Schemas to XML DTDs with Constraints. In: Proceedings of the First International Multi-Symposiums on Computer and Computational Sciences, pp. 528–533 (2006)Google Scholar
  12. 12.
    Murata, M., Lee, D., Mani, M., Kawaguchi, K.: Taxonomy of XML schema languages using formal language theory. ACM Trans. Internet Technol. 5(4), 660–704 (2005)CrossRefGoogle Scholar
  13. 13.
    Sperberg-McQueen, C.M., Thompson, H.: XML Schema. Technical report, World Wide Web Consortium (2005),
  14. 14.
    Vincent, M.W., Liu, J., Liu, C.: Strong functional dependencies and their application. to normal forms in XML. ACM ToDS 29, 445–462 (2004)CrossRefGoogle Scholar
  15. 15.
    Wang, J.: A Comparative Study of Functional Dependencies for XML. In: Zhang, Y., Tanaka, K., Yu, J.X., Wang, S., Li, M. (eds.) APWeb 2005. LNCS, vol. 3399, pp. 308–319. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Gyula I. Szabó
    • 1
  • András Benczúr
    • 1
  1. 1.Faculty of InformaticsEötvös Loránd UniversityBudapestHungary

Personalised recommendations