no. 3
A general framework for the derivation of regular expressions
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 3, pp. 281-305.

The aim of this paper is to design a theoretical framework that allows us to perform the computation of regular expression derivatives through a space of generic structures. Thanks to this formalism, the main properties of regular expression derivation, such as the finiteness of the set of derivatives, need only be stated and proved one time, at the top level. Moreover, it is shown how to construct an alternating automaton associated with the derivation of a regular expression in this general framework. Finally, Brzozowski's derivation and Antimirov's derivation turn out to be a particular case of this general scheme and it is shown how to construct a DFA, a NFA and an AFA for both of these derivations.

DOI : 10.1051/ita/2014010
Classification : 68Q45
Mots clés : regular expressions, alternating automata, derivation, partial derivation 
@article{ITA_2014__48_3_281_0,
     author = {Caron, Pascal and Champarnaud, Jean-Marc and Mignot, Ludovic},
     title = {A general framework for the derivation of regular expressions},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {281--305},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {3},
     year = {2014},
     doi = {10.1051/ita/2014010},
     mrnumber = {3302489},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita/2014010/}
}
TY  - JOUR
AU  - Caron, Pascal
AU  - Champarnaud, Jean-Marc
AU  - Mignot, Ludovic
TI  - A general framework for the derivation of regular expressions
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2014
SP  - 281
EP  - 305
VL  - 48
IS  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ita/2014010/
DO  - 10.1051/ita/2014010
LA  - en
ID  - ITA_2014__48_3_281_0
ER  - 
%0 Journal Article
%A Caron, Pascal
%A Champarnaud, Jean-Marc
%A Mignot, Ludovic
%T A general framework for the derivation of regular expressions
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2014
%P 281-305
%V 48
%N 3
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ita/2014010/
%R 10.1051/ita/2014010
%G en
%F ITA_2014__48_3_281_0
Caron, Pascal; Champarnaud, Jean-Marc; Mignot, Ludovic. A general framework for the derivation of regular expressions. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 3, pp. 281-305. doi : 10.1051/ita/2014010. http://www.numdam.org/articles/10.1051/ita/2014010/

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

[2] V.M. Antimirov and P.D. Mosses, Rewriting extended regular expressions. Theoret. Comput. Sci. 143 (1995) 51-72. | MR | Zbl

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

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

[5] J.A. Brzozowski, Quotient complexity of regular languages. J. Automata, Languages and Combinatorics 15 (2010) 71-89.

[6] J.A. Brzozowski and E.L. Leiss, On equations for regular languages, finite automata, and sequential networks. Theoret. Comput. Sci. 10 (1980) 19-35. | MR | Zbl

[7] P. Caron, J.-M. Champarnaud and L. Mignot, Partial derivatives of an extended regular expression, in LATA, vol. 6638 of Lect. Notes Comput. Sci. Edited by A.H. Dediu, S. Inenaga and C. Martín-Vide. Springer (2011) 179-191.

[8] J.-M. Champarnaud, F. Ouardi and D. Ziadi, An efficient computation of the equation K-automaton of a regular K-expression. Fundam. Inform. 90 (2009) 1-16. | MR | Zbl

[9] J.-M. Champarnaud and D. Ziadi, Canonical derivatives, partial derivatives, and finite automaton constructions. Theoret. Comput. Sci. 239 (2002) 137-163. | MR | Zbl

[10] J. Clarke, An algorithm for RELAX NG validation. Implementation Report (2002).

[11] J.-H. Conway, Regular algebra and finite machines. Chapman and Hall (1971). | Zbl

[12] A. Ginzburg, A procedure for checking equality of regular expressions. J. ACM 14 (1967) 355-362. | Zbl

[13] L. Ilie and S. Yu, Follow automata. Inf. Comput. 186 (2003) 140-162. | MR | Zbl

[14] D. Krob, Differentation of K-rational expressions. Internat. J. Algebra Comput. 2 (1992) 57-87. | MR | Zbl

[15] S. Lombardy and J. Sakarovitch, Derivatives of rational expressions with multiplicity. Theoret. Comput. Sci. 332 (2005) 141-177. | MR | Zbl

[16] M. Might, D. Darais and D. Spiewak, Parsing with derivatives: a functional pearl, in ICFP, edited by M.M.T. Chakravarty, Zh. Hu and O. Danvy. ACM (2011) 189-195.

[17] J. Myhill, Finite automata and the representation of events. WADD TR-57-624 (1957) 112-137.

[18] A. Nerode, Linear automata transformation, in Proc. of AMS 9 (1958) 541-544. | Zbl

[19] S. Owens, J.H. Reppy and A. Turon, Regular-expression derivatives re-examined. J. Funct. Program. 19 (2009) 173-190. | MR | Zbl

[20] J. Sakarovitch, The language, the expression, and the (small) automaton, in CIAA, vol. 3845 of Lect. Notes Comput. Sci. Edited by J. Farré, I. Litovsky and S. Schmitz. Springer (2005) 15-30. | MR | Zbl

[21] M. Sulzmann and K.Z.M. Lu, Partial derivative regular expression pattern matching. Manuscript (2007).

[22] K. Thompson, Regular expression search algorithm. Comm. ACM 11 (1968) 419-422. | Zbl

Cité par Sources :