From Regular Weighted Expressions to Finite Automata

  • Jean-Marc Champarnaud
  • Éric Laugerotte
  • Faissal Ouardi
  • Djelloul Ziadi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2759)


In this article we generalize the concepts of position automaton and ZPC structure to the regular \( \mathbb{K} \) -expressions. We show that the ZPC structure can be built in linear time in the size of the expression and that the associated position automaton can be deduced from it in quadratic time.


Linear Time Regular Expression Formal Series Finite Automaton Syntax Tree 
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  1. [1]
    V. Antimirov, Partial Derivatives of Regular Expressions and Finite Automaton Constructions, Theort. Comput. Sci. 155 (1996), 291–319.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    J. Berstel and C. Reutenauer, Rational series and their languages, Springer-Verlag, Berlin, (1988).zbMATHGoogle Scholar
  3. [3]
    P. Caron and M. Flouret, Glushkov construction for multiplicities, In: S. Yu, A. Paun (eds.), Proc. 5th Int. Conf. on Implementations and Applications of Automata (CIAA). Lecture Notes in Computer Science 2088, Springer-Verlag, (2001), 67–79.CrossRefGoogle Scholar
  4. [4]
    J.-M. Champarnaud, Subset Construction Complexity for Homogeneous Automata, Position Automata and ZPC-Structures, Theoret. Comp. Sc., 267(2001), 17–34.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    J.-M. Champarnaud and D. Ziadi, Computing the Equation Automaton of Regular Expression in O(s 2) space and time, in CPM 2001, Combinatorial Pattern Matching, Lecture Notes in Computer Science, A. Amir and G.M. Landau eds., Springer-Verlag, 2089 (2001), 157–168.Google Scholar
  6. [6]
    V.-M. Glushkov, The abstract theory of automata, Russian Mathematical Surveys, 16 (1961), 1–53.Google Scholar
  7. [7]
    U. Hebisch and H. J. Weinert, Semirings-algebraic theory and applications in computer science, World Scientific, Singapore, (1993).zbMATHGoogle Scholar
  8. [8]
    W. Kuich and J. Salomaa, Semirings, automata, languages. Springer-Verlag, Berlin, (1986).zbMATHGoogle Scholar
  9. [9]
    S. Lombardy and J. Sakarovitch, Derivatives of regular expression with multiplicity, Research report of ENST, 2001D001, (2001).Google Scholar
  10. [10]
    R. F. McNaughton and H. Yamada, Regular expressions and state graphs for automata, IEEE Tans. Electronic Comput. 9 (1960), 39–47.CrossRefGoogle Scholar
  11. [11]
    M. P. Schützenberger, On the definition of a family of automata. Information and control 6 (1961), 245–270.Google Scholar
  12. [12]
    D. Ziadi, J.-L. Ponty, J.-M. Champarnaud, Passage d’une expression rationnelle à un automate fini non-déterministe, Bull. Bel. Math. Soc., 4 (1997), 177–203.zbMATHMathSciNetGoogle Scholar
  13. [13]
    D. Ziadi, Quelques Aspects Théoriques et Algorithmiques des Automates, Thèse d’habilitation à diriger des recherches. Université de Rouen, (2002).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jean-Marc Champarnaud
    • 1
  • Éric Laugerotte
    • 1
  • Faissal Ouardi
    • 1
  • Djelloul Ziadi
    • 1
  1. 1.L.I.F.A.R.University of RouenFrance

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