Skip to main content
SpringerLink
Log in

Functional dependencies on extended relations defined by regular languages

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

Functional dependency (FD) is one of the most analyzed integrity constraints for any data model. In the relational data model, FDs are defined in a natural way: the values of an attribute set Y depend on the values of another attribute set X, that is, “Y is a function of X”. FDs are well studied and are widely used in normalization theory. XML functional dependencies (XFD) can be defined in different ways and no universally best definition has been proposed. They are defined by very intricate concepts, and they are mostly based upon XML elements described by XML schema languages such as a DTD or an XML Schema definition. The instances of these elements are semi-structured tuples. A semi-structured tuple is an ordered list of (attribute: value) pairs. We may think of a tuple as a sentence of a formal language, where the values are the terminal symbols and the attribute names are the nonterminal symbols. In this way, the sequence of the attribute names is the left side of a production rule used to accept the next terminal symbol, that is, the next value of the tuple. So the list of values forms the sentence and the list of attributes forms the dual sentence. In this paper, we introduce the notion of the extended tuple as a sentence from a regular language generated by a grammar where the nonterminal symbols of the grammar are the attribute names of the tuple. Sets of extended tuples are the extended relations (relations are instances). We then introduce the dual language, which generates the tuple types allowed to occur in extended relations. We define functional dependencies over extended relations. The syntax of functional dependencies will be given on the graph of the finite state automaton accepting the regular language. Using this model, we can also handle extended relations generated by recursive regular expressions. The implication problem of our class of dependencies is decidable and finitely axiomatizable by a version of the Chase algorithm performed on the graph of the associated finite state automaton.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley (1995)

  2. Amano, S., Libkin, L., Murlak, F.: XML schema mappings. In: Proc. PODS, pp. 33–42 (2009)

  3. Arenas, M., Libkin, L.: A normal form for XML documents. ACM Trans. Datab. Syst. 29, 195–232 (2004)

    Article  Google Scholar 

  4. Atzeni, P., Morfuni, N.: Functional dependencies and constraints on null values in database relations. Inf. Control 70(1), 1–31 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  5. Berry, G., Sethi, R.: From regular expressions to deterministic automata. Theor. Comput. Sci. 48, 117–126 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  6. Brzozowski, J.A.: Derivatives of regular expressions. J. ACM 11(4), 481–494 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  7. Buneman, P., Davidson, S.B., Fan, W., Hara, C.S., Tan, W.C.: Keys for XML. Comput. Netw. 39(5), 473–487 (2002)

    Article  Google Scholar 

  8. Buneman, P., Davidson, S.B., Fan, W., Hara, C.S., Tan, W.C.: Reasoning about keys for XML. Inf. Syst. 28(8), 1037–1063 (2003)

    Article  Google Scholar 

  9. Champarnaud, J.-M., Ziadi, D.: Canonical derivatives, partial derivatives and finite automaton constructions. Theor. Comput. Sci. 289(1), 137–163 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. 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)

  11. Davidson, S., Fan, W., Hara, C.: Propagating XML constraints to relations. J. Comput. Syst. Sci. 73(3), 316–361 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Fagin, R.: Functional dependencies in a relational database and propositional logic. IBM J. Res. Develop. 21(6), 543–544 (1977)

    Article  MathSciNet  Google Scholar 

  13. Fischer, P.C., Saxton, L.V., Thomas, S.J., Van Gucht, D.: Interactions between dependencies and nested relational structures. J. Comput. Syst. Sci. 31(3), 343–354 (1985)

    Article  MATH  Google Scholar 

  14. Glushkov, V.M.: The abstract theory of automata. Russ. Math. Surv. 16, 1–53 (1961)

    Article  Google Scholar 

  15. Hara, C.S., Davidson, S.B.: Reasoning about nested functional dependencies. In: Proc. PODS, pp. 91–100 (1999)

  16. Hartmann, S., Link, S: More functional dependencies for XML. In: Proc. ADBIS, pp. 355–369 (2003)

  17. Hartmann, S., Link, S., Schewe, K-D.: Functional dependencies over XML documents with DTDs. Acta Cybern. 17(1), 153–171 (2005)

    MATH  MathSciNet  Google Scholar 

  18. Hartmann, S., Link, S., Schewe, K-D.: Axiomatisation of functional dependencies in the presence of records, lists, sets and multisets. Theor. Comput. Sci. 355, 167–196 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  19. Hartmann, S., Link, S: Characterising nested database dependencies by fragments of propositional logic. Ann. Pure Appl. Logic 152, 84–106 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  20. Hartmann, S., Link, S.: Efficient reasoning about a robust XML key fragment. ACM Trans. Datab. Syst. 34(2), 1–33 (2009)

    Article  Google Scholar 

  21. Hartmann, S., Link, S: Numerical constraints on XML data. Inf. Comput. 208(5), 521–544 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  22. Hartmann, S., Köhler, H., Trinh, T.: On the existence of Armstrong data trees for XML functional dependencies. In: Proc. FoIKS LNCS, vol. 5956, pp. 94–113 (2010)

  23. Hartmann, S., Link, S., Trinh, T.: Solving the implication problem for XML functional dependencies with properties. In: Logic, Language, Information and Computation, 17th International Workshop, WoLLIC, pp. 161–175 (2010)

  24. Kot, L., White, W.: Characterization of the interaction of XML functional dependencies with DTDs. In: Proc. ICDT, pp. 119–133 (2007)

  25. Lee, D., Mani, M., Murata, M.: Reasoning about XML schema languages using formal language theory. Technical Report, IBM Almaden Research Center (2000). http://www.cs.ucla.edu/dongwon/paper

  26. Liu, C., Vincent, M.W., Liu, J.: Constraint preserving transformation from relational schema to XML schema. WWW 9(1), 93–110 (2006)

    Article  MathSciNet  Google Scholar 

  27. Lv, T., Yan, P.: Mapping relational schemas to XML DTDs with constraints. In: Proc. First International Multi-Symposiums on Computer and Computational Sciences, pp. 528–533 (2006)

  28. 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)

    Article  Google Scholar 

  29. Nicaud, C., Pivoteau, C., Razet, B.: Average analysis of Glushkov automata under a BST-like model. In: Proc. FSTTCS, pp. 388–399 (2010)

  30. Sali, A., Schewe, K-D.: Counter-free keys and functional dependencies in higher-order datamodels. Fundam. Inform. 70(3), 277–301 (2006)

    MATH  MathSciNet  Google Scholar 

  31. Sperberg-McQueen, C.M., Thompson, H.: XML schema. Technical report, World Wide Web Consortium (2005). http://www.w3.org/XML/Schema

  32. Szabó, G.I., Benczúr, A.: Functional dependencies on extended relations defined by regular languages. In: Proc. FoIKS LNCS, vol. 7153, pp. 385–404 (2012)

  33. Vincent, M.W., Liu, J., Liu, C.: Strong functional dependencies and their application to normal forms in XML. ACM Trans. Datab. Syst. 29, 445–462 (2004)

    Article  Google Scholar 

  34. Vincent, M.W., Liu, J., Mohania, M.K.: On the equivalence between FDs in XML and FDs in relations. Acta Informatica 44, 207–247 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  35. Wang, J.: A comparative study of functional dependencies for XML. In: APWeb, pp. 308–319 (2005)

  36. Wang, J., Topor, R.W.: Removing XML data redundancies using functional and equality-generating dependencies. In: Proc. ADC 2005, pp. 65–74 (2005)

  37. Watson, B.W.: A taxonomy of finite automata construction algorithms. In: Computing Science Note, pp. 93–43. Eindhoven University of Technology, The Netherlands (1993)

    Google Scholar 

  38. Yu, C., Jagadish, H.V.: XML schema refinement through redundancy detection and normalization. VLDB J. 17(2), 203–223 (2008)

    Article  Google Scholar 

  39. Zhou, R., Liu, C., Li, J.: Holistic constraint-preserving transformation from relational schema into XML schema. In: Proc. DSFAA, pp. 4–18 (2008)

Download references

Author information

Authors and Affiliations

  1. Faculty of Informatics, Eötvös Loránd University, Pázmány Péter sétány, 1/C, 1118, Budapest, Hungary

    Gyula I. Szabó & András Benczúr

Authors
  1. Gyula I. Szabó
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. András Benczúr
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gyula I. Szabó.

Additional information

The research was supported by the European Union and co-financed by the European Social Fund (grant agreement no. TAMOP 4.2.2./B-10/1/KMR-2010-0030).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Szabó, G.I., Benczúr, A. Functional dependencies on extended relations defined by regular languages. Ann Math Artif Intell 73, 205–243 (2015). https://doi.org/10.1007/s10472-013-9352-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-013-9352-z

Keywords

Mathematics Subject Classification (2010)

Search

Navigation