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From Regular Weighted Expressions to Finite Automata

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Implementation and Application of Automata (CIAA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2759))

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Abstract

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.

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References

  1. V. Antimirov, Partial Derivatives of Regular Expressions and Finite Automaton Constructions, Theort. Comput. Sci. 155 (1996), 291–319.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. Berstel and C. Reutenauer, Rational series and their languages, Springer-Verlag, Berlin, (1988).

    MATH  Google Scholar 

  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.

    Chapter  Google Scholar 

  4. J.-M. Champarnaud, Subset Construction Complexity for Homogeneous Automata, Position Automata and ZPC-Structures, Theoret. Comp. Sc., 267(2001), 17–34.

    Article  MATH  MathSciNet  Google Scholar 

  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. V.-M. Glushkov, The abstract theory of automata, Russian Mathematical Surveys, 16 (1961), 1–53.

    Google Scholar 

  7. U. Hebisch and H. J. Weinert, Semirings-algebraic theory and applications in computer science, World Scientific, Singapore, (1993).

    MATH  Google Scholar 

  8. W. Kuich and J. Salomaa, Semirings, automata, languages. Springer-Verlag, Berlin, (1986).

    MATH  Google Scholar 

  9. S. Lombardy and J. Sakarovitch, Derivatives of regular expression with multiplicity, Research report of ENST, 2001D001, (2001).

    Google Scholar 

  10. R. F. McNaughton and H. Yamada, Regular expressions and state graphs for automata, IEEE Tans. Electronic Comput. 9 (1960), 39–47.

    Article  Google Scholar 

  11. M. P. Schützenberger, On the definition of a family of automata. Information and control 6 (1961), 245–270.

    Google Scholar 

  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.

    MATH  MathSciNet  Google Scholar 

  13. D. Ziadi, Quelques Aspects Théoriques et Algorithmiques des Automates, Thèse d’habilitation à diriger des recherches. Université de Rouen, (2002).

    Google Scholar 

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© 2003 Springer-Verlag Berlin Heidelberg

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Champarnaud, JM., Laugerotte, É., Ouardi, F., Ziadi, D. (2003). From Regular Weighted Expressions to Finite Automata. In: Ibarra, O.H., Dang, Z. (eds) Implementation and Application of Automata. CIAA 2003. Lecture Notes in Computer Science, vol 2759. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45089-0_6

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  • DOI: https://doi.org/10.1007/3-540-45089-0_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40561-0

  • Online ISBN: 978-3-540-45089-4

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