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An Efficient Computation of the Equation K-automaton of a Regular K-expression

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The aim of this paper is to describe a quadratic algorithm for computing the equation K-automaton of a regular K-expression as defined by Lombardy and Sakarovitch. Our construction is based on an extension to regular K-expressions of the notion of c-continuation that we introduced to compute the equation automaton of a regular expression as a quotient of its position automaton.
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1--16
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bibliogr. 28 poz.
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autor
Bibliografia
  • [1] C. Allauzen and M. Mohri. A Unified Construction of the Glushkov, Follow, and Antimirov Automata. In MFCS-2006, Lecture Notes in Computer Science, R. Kralovic and P. Urzyczyn eds., 4162:110-121, 2006.
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  • [5] P. Caron and M. Flouret, Glushkov construction for series : The non commutative case, Intern. Journ. Comput. Maths, 80(4): 457-472, 2003.
  • [6] J.-M. Champarnaud, E. Laugerotte, F. Ouardi, and D. Ziadi, From Regular Weighted Expressions to Finite Automata, Intern. Journ. of Found. Comput. Sci., (15)5: 687-700, 2004.
  • [7] J.-M. Champarnaud, F. Nicart and D. Ziadi. From the ZPC -structure of a regular expression to its follow automaton, Intern. Journ. of Alg. and Comp., 16(1): pp 17-34, 2006.
  • [8] J.-M. Champarnaud, F. Ouardi and D. Ziadi. Follow automaton versus equation automaton, In: DCFS-2004, Descriptional Complexity of Formal Systems Workshop, Proceedings, L. Ilie and D. Wotschke (eds.), pp. 145-153, 2004.
  • [9] J.-M. Champarnaud, F. Ouardi and D. Ziadi. Normalized expressions and finite automata, Intern. Journ. Of Alg. and Comp., 17-1(2007), 141-154.
  • [10] J.-M. Champarnaud and D. Ziadi. From Mirkin-s Prebases to Antimirov-s Word Partial Derivatives. Informatica Fundamentae, 45(3):195-205, 2001.
  • [11] J.-M. Champarnaud and D. Ziadi. Canonical derivatives and finite automaton constructions, Theoret. Compt. Sci., 289:137-163, 2002.
  • [12] J.-M. Champarnaud and D. Ziadi. Fromc-continuations to new quadratic algorithms for automaton synthesis, Intern. Journ. of Alg. and Comp., 11(6), 707-735, 2001.
  • [13] J.-M. Champarnaud, F. Ouardi and D. Ziadi. An efficient computation of the equation K-automaton of a regularK-expression, in DLT-2007, Lecture Notes in Computer Science, T. Harju, J. Karhumäki and A. Lepistö eds., Springer-Verlag Berlin Heidelberg, 4588(2007), 145-156.
  • [14] C.-H. Chang and R. Paige. From Regular Expressions to DFA-s Using Compressed NFA-s, Theoret. Comput. Sci., 178, 1-36, 1997.
  • [15] T. Claveirole, S. Lombardy, S. O-Connor, L.-N. Pouchet, and J. Sakarovitch, Inside Vaucanson, Proc. Of CIAA-2005 (J. Farré, I. Litovsky and S. Schmitz eds.), Lect. Notes in Comp. Sci., 3845, Springer (2006), 116-128.
  • [16] V.-M. Glushkov. The abstract theory of automata, Russian Mathematical Surveys, 16, 1-53, 1961.
  • [17] U. Hebisch and H. J. Weinert. Semirings: algebraic theory and applications in computer science, World Scientific, Singapore, 1993.
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  • [19] W. Kuich and A. Salomaa. Semirings, automata, languages. EATCS Monographs on Theoretical Computer Science, Volume 5. Springer-Verlag, Berlin, 1986. Princeton U. Press.
  • [20] S. Lombardy and J. Sakarovitch. Derivations of Rational Expressions with Multiplicity. MFCS-2002, K. Diks andW. Ritter, eds., Lect. Notes in Comp. Sci., Springer, 2420: 471-482, 2002.
  • [21] S. Lombardy and J. Sakarovitch. Derivatives of Rational Expressions with Multiplicity. Theoret. Comput. Sci., 332: 141-177, 2005.
  • [22] R. F. McNaughton and H. Yamada, Regular expressions and state graphs for automata, IEEE Trans. Electronic Comput. 9: 39-47, 1960.
  • [23] B. G. Mirkin. An algorithm for constructing a base in a language of regular expressions. Engineering Cybernetics, 5:110-116, 1966.
  • [24] J. Sakarovitch. Éléments de la théorie des automates. Les classiques de l-informatique., Vuibert Paris, 2003.
  • [25] M. P. Schützenberger. On the definition of a family of automata. Information and control, 6:245-270, (1961).
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  • [27] D. Ziadi, J.-L. Ponty, and J.-M. Champarnaud. Passage d-une expression rationnelle à un automate fini non-déterministe. Bull. Belg. Math. Soc., 4:177-203, 1997.
  • [28] D. Ziadi, Quelques aspects théoriques et algorithmiques des automates. Thèse d-habilitation à diriger des recherches, Université de Rouen, 2002.
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Bibliografia
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bwmeta1.element.baztech-article-BUS8-0004-0001
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