Abstract
The aim of this paper is to describe a quadratic algorithm to compute the equation \(\mathbb{K}\)-automaton of a regular \(\mathbb{K}\)-expression as defined by Lombardy and Sakarovitch. Our construction is based on an extension to regular \(\mathbb{K}\)-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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References
Allauzen, C., Mohri, M.: A Unified Construction of the Glushkov, Follow, and Antimirov Automata. In: Královič, R., Urzyczyn, P. (eds.) MFCS 2006. LNCS, vol. 4162, pp. 110–121. Springer, Heidelberg (2006)
Antimirov, V.: Partial derivatives of regular expressions and finite automaton constructions. Theoret. Comput. Sci. 155, 291–319 (1996)
Brüggemann-Klein, A.: Regular Expressions into Finite Automata. Theoret. Comput. Sci. 120, 197–213 (1993)
Berstel, J., Reutenauer, C.: Les séries rationnelles et leurs langages. In: Études et recherches en informatique, Masson, Paris, 1984, Springer, Berlin Heidelberg English version: Rational series and their languages (1988)
Caron, P., Flouret, M.: Glushkov construction for series: The non commutative case. Intern. Journ. Comput. Maths 80(4), 457–472 (2003)
Champarnaud, J.-M., Laugerotte, E., Ouardi, F., Ziadi, D.: From Regular Weighted Expressions to Finite Automata. Intern. Journ. of Found. Comput. Sci. 5(15), 687–700 (2004)
Champarnaud, J.-M., Nicart, F., Ziadi, D.: From the ZPC-structure of a regular expression to its follow automaton. Intern. Journ. of Alg. and Comp. 16(1), 17–34 (2006)
Champarnaud, J.-M., Ouardi, F., Ziadi, D.: Follow automaton versus equation automaton. In: Ilie, L., Wotschke, D. (eds.) DCFS 2004, Descriptional Complexity of Formal Systems Workshop, Proceedings, pp. 145–153 (2004)
Champarnaud, J.-M., Ouardi, F., Ziadi, D.: Normalized expressions and finite automata, Intern. Journ. of Alg. and Comp. (to appear)
Champarnaud, J.-M., Ziadi, D.: From Mirkin’s Prebases to Antimirov’s Word Partial Derivatives. Informatica Fundamentae 45(3), 195–205 (2001)
Champarnaud, J.-M., Ziadi, D.: Canonical derivatives and finite automaton constructions. Theoret. Compt. Sci. 289, 137–163 (2002)
Champarnaud, J.-M., Ziadi, D.: From c-continuations to new quadratic algorithms for automaton synthesis. Intern. Journ. of Alg. and Comp. 11(6), 707–735 (2001)
Chang, C.-H., Paige, R.: From Regular Expressions to DFA’s Using Compressed NFA’s. Theoret. Comput. Sci. 178, 1–36 (1997)
Claveirole, T., Lombardy, S., O’Connor, S., Pouchet, L.-N., Sakarovitch, J.: Inside Vaucanson. In: Farré, J., Litovsky, I., Schmitz, S. (eds.) CIAA 2005. LNCS, vol. 3845, pp. 116–128. Springer, Heidelberg (2006)
Glushkov, V.-M.: The abstract theory of automata. Russian Mathematical Surveys 16, 1–53 (1961)
Hebisch, U., Weinert, H.J.: Semirings: algebraic theory and applications in computer science. World Scientific, Singapore (1993)
Ilie, L., Yu, S.: Follow automata. Information and computation 186, 140–162 (2003)
Kuich, W., Salomaa, A.: Semirings, automata, languages. In: EATCS Monographs on Theoretical Computer Science, vol. 5, Springer-Verlag, Berlin Heidelberg (1986) Princeton U. Press
Lombardy, S., Sakarovitch, J.: Derivations of Rational Expressions with Multiplicity. In: Diks, K., Ritter, W. (eds.) MFCS 2002. LNCS, vol. 2420, pp. 471–482. Springer, Heidelberg (2002)
Lombardy, S., Sakarovitch, J.: Derivatives of Rational Expressions with Multiplicity. Theoret. Comput. Sci. 332, 141–177 (2005)
McNaughton, R.F., Yamada, H.: Regular expressions and state graphs for automata. IEEE Trans. Electronic Comput. 9, 39–47 (1960)
Mirkin, B.G.: An algorithm for constructing a base in a language of regular expressions. Engineering Cybernetics 5, 110–116 (1966)
Sakarovitch, J.: Éléments de la théorie des automates. Les classiques de l’informatique, Vuibert Paris (2003)
Schützenberger, M.P.: On the definition of a family of automata. Information and control 6, 245–270 (1961)
Thompson, K.: Regular expression search algorithm. Comm. ACM 11(6), 419–422 (1968)
Ziadi, D., Ponty, J.-L., Champarnaud, J.-M.: Passage d’une expression rationnelle à un automate fini non-déterministe. Bull. Belg. Math. Soc. 4, 177–203 (1997)
Ziadi, D.: Quelques aspects théoriques et algorithmiques des automates. Thèse d’habilitation à diriger des recherches, Université de Rouen (2002)
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Champarnaud, JM., Ouardi, F., Ziadi, D. (2007). An Efficient Computation of the Equation \(\mathbb{K}\)-Automaton of a Regular \(\mathbb{K}\)-Expression. In: Harju, T., Karhumäki, J., Lepistö, A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73208-2_16
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DOI: https://doi.org/10.1007/978-3-540-73208-2_16
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