Abstract
This paper introduces an efficient weighted regognition algorithm. It is based on a suitable tree structure called ZPC without building the position automaton. The ZPC-structure results from the compact language and the polynomial structure of weighted expressions. We show that the time complexity of this algorithm is the best oneuntil now.
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References
Abbad, H., Laugerotte, É.: Symbolic demonstrations in MuPAD-Combinat. INFOCOMP Journal of Computer Science 7, 21–30 (2008)
Berstel, J., Reutenauer, C.: Rational series and their languages. Springer, Berlin (1988)
Bloom, S.L., Ésik, Z.: Iteration theories. Springer, Berlin (1993)
Bloom, S.L., Ésik, Z., Kuich, W.: Partial Conway and iteration semirings. Fundamenta Informaticae 86, 19–40 (2008)
Caron, P., Flouret, M.: Glushkov construction for multiplicities. In: Yu, S., Păun, A. (eds.) CIAA 2000. LNCS, vol. 2088, pp. 67–79. Springer, Heidelberg (2001)
Champarnaud, J.M., Duchamp, G.: Derivatives of rational expressions and related theorems. Theoretical Computer Science 313, 31–44 (2004)
Champarnaud, J.M., Laugerotte, É., Ouardi, F., Ziadi, D.: From regular weighted expressions to finite automata. International Journal of Foundations of Computer Science 15, 687–699 (2004)
Conway, J.C.: Regular algebra and finite machines. Chapman and Hall, London (1971)
Droste, M., Kuich, W., Vogler, H.: Handbook of weighted automata. Springer, Berlin (2009)
Duchamp, G., Flouret, M., Laugerotte, É., Luque, J.G.: Direct and dual laws for automata with multiplicities. Theoretical Computer Science 267, 105–120 (2001)
Golan, J.S.: Semirings and their applications. Kluwer Academic Publishers Dordrecht (1999)
Hivert, H., Thiéry, N.M.: MuPAD-Combinat, an open-source package for research in algebraic combinatorics. Séminaire Lotharingien de Combinatoire, 1–70 (2004)
Kleene, S.C.: Representation of events in nerve nets and finite automata. Automata Studies, 3–42 (1956)
Krob, D.: Models of a K-rational identity system. Journal of Computer and System Sciences 45, 396–434 (1992)
Laugerotte, É., Ziadi, D.: Weighted word recognition. Fundamenta Informaticae 83, 277–298 (2008)
Lombardy, S., Sakarovitch, J.: Derivatives of rational expressions with multiplicity. Theoretical Computer Science 332, 141–177 (2005)
Sakarovitch, J.: Éléments de théorie des automates. Vuibert (2003)
Salomaa, A., Soittola, M.: Automata-theoretic aspects of formal power series. Springer, Berlin (1978)
Schützenberger, M.P.: On the definition of a family of automata. Information and Control 4, 245–270 (1961)
Ziadi, D., Ponty, J.L., Champarnaud, J.M.: Passage d’une expression rationnelle à un automate fini non-déterministe. Bulletin of the Belgian Mathematical Society 4, 177–203 (1997)
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Abbad, H., Laugerotte, É. (2013). Computing Weights. In: Konstantinidis, S. (eds) Implementation and Application of Automata. CIAA 2013. Lecture Notes in Computer Science, vol 7982. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39274-0_4
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DOI: https://doi.org/10.1007/978-3-642-39274-0_4
Publisher Name: Springer, Berlin, Heidelberg
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