How expressions can code for automata
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 39 (2005) no. 1, pp. 217-237.

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.

DOI: 10.1051/ita:2005013
Classification: 68Q45,  68Q70
Keywords: finite automata, regular expression, derivation of expressions, quotient of automata
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Lombardy, Sylvain; Sakarovitch, Jacques. How expressions can code for automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 39 (2005) no. 1, pp. 217-237. doi : 10.1051/ita:2005013. http://www.numdam.org/articles/10.1051/ita:2005013/

[1] V. Antimirov, Partial derivatives of regular expressions and finite automaton constructions. Theor. Comput. Sci. 155 (1996) 291-319. | Zbl

[2] A. Arnold, Systèmes de transitions finis et sémantique des processus communiquants. Masson (1992). English Trans.: Finite Transitions Systems, Prentice-Hall (1994). | Zbl

[3] G. Berry and R. Sethi, From regular expressions to deterministic automata. Theor. Comput. Sci. 48 (1986) 117-126. | Zbl

[4] J. Berstel and J.-E. Pin, Local languages and the Berry-Sethi algorithm. Theor. Comput. Sci. 155 (1996) 439-446. | Zbl

[5] A. Brügemann-Klein, Regular expressions into finite automata. Theor. Comput. Sci. 120 (1993) 197-213. | Zbl

[6] J.A. Brzozowski, Derivatives of regular expressions. J. Assoc. Comput. Mach. 11 (1964) 481-494. | Zbl

[7] P. Caron and D. Ziadi, Characterization of Glushkov automata. Theor. Comput. Sci. 233 (2000) 75-90. | Zbl

[8] 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. | Zbl

[9] J.-M. Champarnaud and D. Ziadi, Canonical derivatives, partial derivatives and finite automaton constructions. Theor. Comput. Sci. 289 (2002) 137-163. | Zbl

[10] J.H. Conway, Regular Algebra And Finite Machines. Chapman and Hall (1971). | Zbl

[11] V. Glushkov, The abstract theory of automata. Russian Mathematical Surveys 16 (1961) 1-53. | Zbl

[12] 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.) | Zbl

[13] R. Mcnaughton and H. Yamada, Regular Expressions And State Graphs For Automata. IRE Trans. electronic computers 9 (1960) 39-47. | Zbl

[14] J. Sakarovitch, A construction on automata that has remained hidden. Theor. Comput. Sci. 204 (1998) 205-231. | Zbl

[15] J. Sakarovitch, Éléments de théorie des automates. Vuibert (2003). English Trans.: Cambridge University Press, to appear.

[16] K. Thompson, Regular expression search algorithm. Comm. Assoc. Comput. Mach. 11 (1968) 419-422. | Zbl

[17] D. Wood, Theory Of Computation. Wiley (1987). | MR | Zbl

[18] S. Yu, Regular languages, in Handbook of Formal Languages, edited by G. Rozenberg and A. Salomaa. Elsevier 1 (1997) 41-111.

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