Abstract
We present a new sequential algorithm to convert a regular expression into its Glushkov automaton. This conversion runs in quadratic time, so it has the same time complexity as the Brüggemann-Klein algorithm and the Chang and Paige one. It provides, however, a representation of the Glushkov automaton that needs only linear space.
An extended version is to appear in the Belgian Mathematical Society Bulletin, under the title: “Passage d'une expression rationnelle à un automate fini non déterministe”.
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References
A. Aho, R. Sethi and J-D. Ullman, Compilers, Addison-Wesley Publishing Company, Inc., Reading, Mass., 1986.
A. Aho and J.D. Ullman, Foundations of Computer Science, W.H. Freeman and Company, New York, 1992.
J. Berstel and J-E. Pin, Local languages and the Berry-Sethi algorithm, Theoretical Computer Science, 155: 439–446, 1996.
G. Berry and R. Sethi, From Regular Expression to Deterministic Automata, Theoretical Computer Science, 48: 117–126, 1986.
D. Beauquier, J. Berstel et Ph. Chrétienne, Eléments d'algorithmique, Ed. Masson, Paris, 1992.
A. Brüggemann-Klein, Regular Expressions into Finite Automata, Theoretical Computer Science, 120: 197–213, 1993.
J.-M. Champarnaud and G. Hansel, AUTOMATE, a computing package for automata and finite semigroups, Journal of Symbolic Computation, 12, 197–220, 1991.
C.H. Chang and R. Paige, From regular expressions to dfa's using compressed nfa's. In Apostolico, Crochemore, Galil and Manber editors, LNCS 644: Combinatorial Pattern Matching, Proceedings, 88–108, Springer Verlag, 1992.
V.-M. Glushkov, The abstract theory of automata, Russian Mathematical Surveys, 16, 1–53, 1961.
B.W. Watson, Taxonomies and Toolkits of Regular Language Algorithms, CIF-DATA Koninklijke Bibliotheek, Den Haag, Ph. D., Eindhoven University of Technology, 1995.
D. Ziadi, Algorithmique parallèle et séquentielle des automates, Thèse de doctorat, Université de Rouen, 1996.
D. Ziadi and J.-M. Champarnaud, An optimal parallel algorithm to convert a regular expression into its Glushkov automaton, accepted in Theoretical Computer Science, rapport LIR95.10 Informatique Fondamentale, Université de Rouen, 1995.
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© 1997 Springer-Verlag Berlin Heidelberg
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Ponty, J.L., Ziadi, D., Champarnaud, J.M. (1997). A new quadratic algorithm to convert a regular expression into an automaton. In: Raymond, D., Wood, D., Yu, S. (eds) Automata Implementation. WIA 1996. Lecture Notes in Computer Science, vol 1260. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63174-7_9
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DOI: https://doi.org/10.1007/3-540-63174-7_9
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