Hostname: page-component-74656f9884-g96k6 Total loading time: 0 Render date: 2026-11-10T02:57:13.335Z Has data issue: false hasContentIssue false
  • English
  • Français

Efficient weighted expressions conversion

Published online by Cambridge University Press:  06 September 2007

Faissal Ouardi  and
Djelloul Ziadi
Faissal Ouardi
Affiliation:
L.I.T.I.S., University of Rouen, France; Faissal.Ouardi@univ-rouen.fr; Djelloul.Ziadi@univ-rouen.fr
Djelloul Ziadi
Affiliation:
L.I.T.I.S., University of Rouen, France; Faissal.Ouardi@univ-rouen.fr; Djelloul.Ziadi@univ-rouen.fr
Get access

Abstract

J. Hromkovic et al. have given an elegant method to convert a regular expression of size n into an ε-free nondeterministic finite automaton having O(n) states and O(nlog2 (n)) transitions. This method has been implemented efficiently in O(nlog2 (n)) time by C. Hagenah and A. Muscholl. In this paper we extend this method to weighted regular expressions and we show that it can be achieved in O(nlog2 (n)) time.

Keywords

Formal languages and automatacomplexity of computation

Information

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 2 , April 2008 , pp. 285 - 307
Copyright
© EDP Sciences, 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Antimirov, V., Partial derivatives of regular expressions and finite automaton constructions. Theoret. Comput. Sci. 155 (1996) 291–319. CrossRef
Brüggemann-Klein, A., Regular expressions into finite automata. Theoret. Comput. Sci. 120 (1993) 197–213. CrossRef
J. Berstel and C. Reutenauer. Rational series and their languages. Springer-Verlag, Berlin (1988).
Caron, P. and Flouret, M., Glushkov construction for series: the non commutative case. Int. J. Comput. Math. 80 (2003) 457–472. CrossRef
Caron, P. and Ziadi, D., Characterization of Glushkov automata. Theoret. Comput. Sci. 231 (2000) 75–90. CrossRef
Champarnaud, J.-M. and Ziadi, D., Computing the equation automaton of regular expression in O(s2 ) space and time, in CPM 2001, Combinatorial Pattern Matching, edited by A. Amir and G.M. Landau. Lect. Notes Comput. Sci. 2089 (2001) 157–168. CrossRef
Champarnaud, J.-M., Laugerotte, E., Ouardi, F. and Ziadi, D., From regular weighted expressions to finite automata. Int. J. Fond. Comput. Sci. 15 (2004) 687–700. CrossRef
Glushkov, V.-M., The abstract theory of automata. Russian Math. Surveys 16 (1961) 1–53. CrossRef
Hagenah, C. and Muscholl, A., Computing ε-free NFA from regular expression in O(nlog2 (n)) time. RAIRO-Theor. Inf. Appl. 34 (2000) 257–277. CrossRef
U. Hebisch and H.J. Weinert, Semirings: algebraic theory and applications in computer science. World Scientific, Singapore (1993).
Hromkovic, U., Seibert, J. and Wilke, T., Translating regular expressions into small ε-free nondeterministic finite automata. J. Comput. System Sci. 62 (2001) 565–588. CrossRef
L. Ilie and S. Yu, Algorithms for computing small NFAs, in Proc 27th MFCS, Warszawa, 2002, edited by K. Diks and W. Rytter. Lect. Notes Comput. Sci. (2002) 328–340.
W. Kuich and J. Salomaa, Semirings, automata, languages. Springer-Verlag, Berlin (1986).
Lombardy, S. and Sakarovitch, J., Derivatives of regular expression with multiplicity, Proc. of MFCS 2002. Lect. Notes Comput. Sci. 2420 (2002) 471–48. CrossRef
McNaughton, R.F. and Yamada, H., Regular expressions and state graphs for automata. IEEE T. Electron. Comput. 9 (1960) 39–47. CrossRef
Schützenberger, M.P., On the definition of a family of automata. Inform. Control 6 (1961) 245–270. CrossRef
D. Ziadi, Algorithmique parallèle et séquentielle des automates. Thesis, LIR report, Université de Rouen (1996).
D. Ziadi, Quelques aspects théoriques et algorithmiques des automates. Thesis, Université de Rouen (2002).
Ziadi, D., Ponty, J.-L. and Champarnaud, J.-M., Passage d'une expression rationnelle à un automate fini non-déterministe. Bull. Belg. Math. Soc. Simon Stevin 4 (1997) 177–203.