Advertisement

Checking Determinism of Regular Expressions with Counting

  • Haiming Chen
  • Ping Lu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7410)

Abstract

We give characterizations of strong determinism for regular expressions with counting, based on which we present an O(|Σ E ||E|) time algorithm to check whether an expression E with counting is strongly deterministic where Σ E is the set of distinct symbols in E. It improves the previous upper bound of O(|E|3) time on the same decision problems for both standard regular expressions and regular expressions with counting. As a natural result of our work we derive a characterization of weak determinism for regular expressions with counting, which leads to a new O(|Σ E ||E|) time algorithm for deciding weak determinism of regular expressions with counting.

Keywords

Time Algorithm Regular Expression Regular Language Syntax Tree Attribute Grammar 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Brüggemann-Klein, A.: Regular expressions into finite automata. Theoretical Computer Science 120(2), 197–213 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Brüggemann-Klein, A., Wood, D.: Deterministic Regular Languages. In: Finkel, A., Jantzen, M. (eds.) STACS 1992. LNCS, vol. 577, pp. 173–184. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  3. 3.
    Brüggemann-Klein, A., Wood, D.: One-unambiguous regular languages. Information and Computation 142(2), 182–206 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Chen, H., Lu, P.: Assisting the Design of XML Schema: Diagnosing Nondeterministic Content Models. In: Du, X., Fan, W., Wang, J., Peng, Z., Sharaf, M.A. (eds.) APWeb 2011. LNCS, vol. 6612, pp. 301–312. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Gelade, W., Gyssens, M., Martens, W.: Regular expressions with counting: weak versus strong determinism. SIAM J. Comput. 41(1), 160–190 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Gelade, W., Neven, F.: Succinctness of the complement and intersection of regular expressions. In: STACS 2008, pp. 325–336 (2008)Google Scholar
  7. 7.
    Hovland, D.: The Membership Problem for Regular Expressions with Unordered Concatenation and Numerical Constraints. In: Dediu, A.-H., Martín-Vide, C. (eds.) LATA 2012. LNCS, vol. 7183, pp. 313–324. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    Kilpeläinen, P.: Checking determinism of XML Schema content models in optimal time. Informat. Systems 36(3), 596–617 (2011)CrossRefGoogle Scholar
  9. 9.
    Kilpeläinen, P., Tuhkanen, R.: Towards efficient implementation of XML Schema content models. In: DocEng 2004, pp. 239–241. ACM, New York (2004)CrossRefGoogle Scholar
  10. 10.
    Kilpeläinen, P., Tuhkanen, R.: One-unambiguity of regular expressions with numeric occurrence indicators. Information and Computation 205(6), 890–916 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Koch, C., Scherzinger, S.: Attribute grammars for scalable query processing on XML streams. The VLDB Journal 16(3), 317–342 (2007)CrossRefGoogle Scholar
  12. 12.
    Martens, W., Neven, F., Schwentick, T.: Complexity of Decision Problems for Simple Regular Expressions. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds.) MFCS 2004. LNCS, vol. 3153, pp. 889–900. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Martens, W., Neven, F., Schwentick, T., Bex, G.J.: Expressiveness and complexity of XML Schema. ACM Transactions on Database Systems 31(3), 770–813 (2006)CrossRefGoogle Scholar
  14. 14.
    Sperberg-McQueen, C.M.: Notes on finite state automata with counters (2004), http://www.w3.org/XML/2004/05/msm-cfa.html

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Haiming Chen
    • 1
  • Ping Lu
    • 1
  1. 1.State Key Laboratory of Computer Science, Institute of SoftwareChinese Academy of SciencesBeijingChina

Personalised recommendations