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
V. Antimirov, Partial Derivatives of Regular Expressions and Finite Automaton Constructions, Theort. Comput. Sci. 155 (1996), 291–319.
J. Berstel and C. Reutenauer, Rational series and their languages, Springer-Verlag, Berlin, (1988).
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.
J.-M. Champarnaud, Subset Construction Complexity for Homogeneous Automata, Position Automata and ZPC-Structures, Theoret. Comp. Sc., 267(2001), 17–34.
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.
V.-M. Glushkov, The abstract theory of automata, Russian Mathematical Surveys, 16 (1961), 1–53.
U. Hebisch and H. J. Weinert, Semirings-algebraic theory and applications in computer science, World Scientific, Singapore, (1993).
W. Kuich and J. Salomaa, Semirings, automata, languages. Springer-Verlag, Berlin, (1986).
S. Lombardy and J. Sakarovitch, Derivatives of regular expression with multiplicity, Research report of ENST, 2001D001, (2001).
R. F. McNaughton and H. Yamada, Regular expressions and state graphs for automata, IEEE Tans. Electronic Comput. 9 (1960), 39–47.
M. P. Schützenberger, On the definition of a family of automata. Information and control 6 (1961), 245–270.
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.
D. Ziadi, Quelques Aspects Théoriques et Algorithmiques des Automates, Thèse d’habilitation à diriger des recherches. Université de Rouen, (2002).
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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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