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How expressions can code for automata

Published online by Cambridge University Press:  15 March 2005

Sylvain Lombardy  and
Jacques Sakarovitch
Sylvain Lombardy
Affiliation:
LIAFA (UMR 7089), Université Paris 7, 2 place Jussieu, 75251 Paris Cedex 05, France; [email protected]
Jacques Sakarovitch
Affiliation:
LTCI (UMR 5141), CNRS/ENST, 46 rue Barrault, 75634 Paris Cedex 13, France; [email protected]
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Abstract

In this paper we investigate how it is possible to recover an automaton from a rational expression that has been computed from that automaton. The notion of derived term of an expression, introduced by Antimirov, appears to be instrumental in this problem. The second important ingredient is the co-minimization of an automaton, a dual and generalized Moore algorithm on non-deterministic automata.
We show here that if an automaton is then sufficiently “decorated”, the combination of these two algorithms gives the desired result. Reducing the amount of “decoration” is still the object of ongoing investigation.

Keywords

Finite automataregular expressionderivation of expressionsquotient of automata.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 39 , Issue 1: Imre Simon, the tropical computer scientist , January 2005 , pp. 217 - 237
Copyright
© EDP Sciences, 2005

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References

Antimirov, V., Partial derivatives of regular expressions and finite automaton constructions. Theor. Comput. Sci. 155 (1996) 291–319. CrossRef
A. Arnold, Systèmes de transitions finis et sémantique des processus communiquants. Masson (1992). English Trans.: Finite Transitions Systems, Prentice-Hall (1994).
Berry, G. and Sethi, R., From regular expressions to deterministic automata. Theor. Comput. Sci. 48 (1986) 117–126. CrossRef
Berstel, J. and Pin, J.-E., Local languages and the Berry-Sethi algorithm. Theor. Comput. Sci. 155 (1996) 439–446. CrossRef
Brügemann-Klein, A., Regular expressions into finite automata. Theor. Comput. Sci. 120 (1993) 197–213. CrossRef
Brzozowski, J.A., Derivatives of regular expressions. J. Assoc. Comput. Mach. 11 (1964) 481–494. CrossRef
Caron, P. and Ziadi, D., Characterization of Glushkov automata. Theor. Comput. Sci. 233 (2000) 75–90. CrossRef
J.-M. Champarnaud and D. Ziadi, New finite automaton constructions based on canonical derivatives, in Pre-Proceedings of CIAA'00 , edited by M. Daley, M. Eramian and S. Yu, Univ. of Western Ontario (2000) 36–43.
Champarnaud, J.-M. and Ziadi, D., Canonical derivatives, partial derivatives and finite automaton constructions. Theor. Comput. Sci. 289 (2002) 137–163. CrossRef
J.H. Conway, Regular Algebra And Finite Machines. Chapman and Hall (1971).
Glushkov, V., The abstract theory of automata. Russian Mathematical Surveys 16 (1961) 1–53. CrossRef
S. Lombardy and J. Sakarovitch, Derivatives of rational expressions with multiplicity. Theor. Comput. Sci., to appear. (Journal version of Proc. MFCS 02, Lect. Notes Comput. Sci. 2420 (2002) 471–482.)
McNaughton, R. and Yamada, H., Regular Expressions And State Graphs For Automata. IRE Trans. electronic computers 9 (1960) 39–47. CrossRef
Sakarovitch, J., A construction on automata that has remained hidden. Theor. Comput. Sci. 204 (1998) 205–231. CrossRef
J. Sakarovitch, Éléments de théorie des automates. Vuibert (2003). English Trans.: Cambridge University Press, to appear.
Thompson, K., Regular expression search algorithm. Comm. Assoc. Comput. Mach. 11 (1968) 419–422.
D. Wood, Theory Of Computation. Wiley (1987).
S. Yu, Regular languages, in Handbook of Formal Languages, edited by G. Rozenberg and A. Salomaa. Elsevier 1 (1997) 41–111.