Multi-Tilde-Bar Derivatives

  • Pascal Caron
  • Jean-Marc Champarnaud
  • Ludovic Mignot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7381)


Multi-tilde-bar operators allow us to extend regular expressions. The associated extended expressions are compatible with the structure of Glushkov automata and they provide a more succinct representation than standard expressions. The aim of this paper is to examine the derivation of multi-tilde-bar expressions. Two types of computation are investigated: Brzozowski derivation and Antimirov derivation, as well as the construction of the associated automata.


Partial Derivative Regular Expression Regular Language Free List Distincts Symbol 
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.
    Almeida, M., Moreira, N., Reis, R.: Antimirov and Mosses’s rewrite system revisited. Int. J. Found. Comput. Sci. 20(4), 669–684 (2009)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Antimirov, V.: Partial derivatives of regular expressions and finite automaton constructions. Theoret. Comput. Sci. 155, 291–319 (1996)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Antimirov, V.M., Mosses, P.D.: Rewriting extended regular expressions. Theor. Comput. Sci. 143(1), 51–72 (1995)MathSciNetMATHGoogle Scholar
  4. 4.
    Berry, G., Sethi, R.: From regular expressions to deterministic automata. Theoret. Comput. Sci. 48(1), 117–126 (1986)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Brzozowski, J.A.: Derivatives of regular expressions. J. Assoc. Comput. Mach. 11(4), 481–494 (1964)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Brzozowski, J.A.: Quotient complexity of regular languages. Journal of Automata, Languages and Combinatorics 15(1/2), 71–89 (2010)Google Scholar
  7. 7.
    Brzozowski, J.A., Leiss, E.L.: On equations for regular languages, finite automata, and sequential networks. Theor. Comput. Sci. 10, 19–35 (1980)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Caron, P., Champarnaud, J.M., Mignot, L.: Erratum to “acyclic automata and small expressions using multi-tilde-bar operators”. [Theoret. Comput. Sci. 411(38-39), 3423–3435] (2010); Theor. Comput. Sci. 412(29), 3795–3796 (2011)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Caron, P., Champarnaud, J.M., Mignot, L.: Multi-bar and multi-tilde regular operators. Journal of Automata, Languages and Combinatorics 16(1), 11–26 (2011)Google Scholar
  10. 10.
    Caron, P., Champarnaud, J.-M., Mignot, L.: Partial Derivatives of an Extended Regular Expression. In: Dediu, A.-H., Inenaga, S., Martín-Vide, C. (eds.) LATA 2011. LNCS, vol. 6638, pp. 179–191. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Caron, P., Champarnaud, J.M., Mignot, L.: A general frame for the derivation of regular expressions (submitted, 2012)Google Scholar
  12. 12.
    Champarnaud, J.-M., Jeanne, H., Mignot, L.: Approximate Regular Expressions and Their Derivatives. In: Dediu, A.-H., Martín-Vide, C. (eds.) LATA 2012. LNCS, vol. 7183, pp. 179–191. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  13. 13.
    Champarnaud, J.M., Ouardi, F., Ziadi, D.: An efficient computation of the equation \(\mathbb{K}\)-automaton of a regular \(\mathbb{K}\)-expression. Fundam. Inform. 90(1-2), 1–16 (2009)MathSciNetMATHGoogle Scholar
  14. 14.
    Champarnaud, J.M., Ziadi, D.: Canonical derivatives, partial derivatives, and finite automaton constructions. Theoret. Comput. Sci. 239(1), 137–163 (2002)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Conway, J.H.: Regular algebra and finite machines. Chapman and Hall (1971)Google Scholar
  16. 16.
    Frishert, M.: FIRE Works & FIRE Station: A finite automata and regular expression playground. Ph.D. thesis, Eindhoven University, Netherlands (2005)Google Scholar
  17. 17.
    Ginzburg, A.: A procedure for checking equality of regular expressions. J. ACM 14(2), 355–362 (1967)MATHCrossRefGoogle Scholar
  18. 18.
    Ilie, L., Yu, S.: Follow automata. Inf. Comput. 186(1), 140–162 (2003)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Kleene, S.: Representation of events in nerve nets and finite automata. Automata Studies Ann. Math. Studies 34, 3–41 (1956)MathSciNetGoogle Scholar
  20. 20.
    Krob, D.: Differentation of K-rational expressions. Internat. J. Algebra Comput. 2(1), 57–87 (1992)MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Lombardy, S., Sakarovitch, J.: Derivatives of rational expressions with multiplicity. Theor. Comput. Sci. 332(1-3), 141–177 (2005)MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Owens, S., Reppy, J.H., Turon, A.: Regular-expression derivatives re-examined. J. Funct. Program. 19(2), 173–190 (2009)MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Sulzmann, M., Lu, K.: Partial derivative regular expression pattern matching (December 2007) (manuscript)Google Scholar
  24. 24.
    Yu, S.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages. Word, Language, Grammar, vol. I, pp. 41–110. Springer, Berlin (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Pascal Caron
    • 1
  • Jean-Marc Champarnaud
    • 1
  • Ludovic Mignot
    • 1
  1. 1.LITISUniversité de RouenSaint-Étienne du Rouvray CedexFrance

Personalised recommendations