Hostname: page-component-76d6cb85b7-vdhp9 Total loading time: 0 Render date: 2026-07-11T15:12:33.598Z Has data issue: false hasContentIssue false
  • English
  • Français

A general framework for the derivation of regularexpressions

Published online by Cambridge University Press:  27 May 2014

Pascal Caron ,
Jean-Marc Champarnaud  and
Ludovic Mignot
Pascal Caron
Affiliation:
LITIS, Université de Rouen, 76801 Saint-Étienne du Rouvray Cedex, France.. pascal.caron@univ-rouen.fr, jean-marc.champarnaud@univ-rouen.fr, ludovic.mignot@univ-rouen.fr
Jean-Marc Champarnaud
Affiliation:
LITIS, Université de Rouen, 76801 Saint-Étienne du Rouvray Cedex, France.. pascal.caron@univ-rouen.fr, jean-marc.champarnaud@univ-rouen.fr, ludovic.mignot@univ-rouen.fr
Ludovic Mignot
Affiliation:
LITIS, Université de Rouen, 76801 Saint-Étienne du Rouvray Cedex, France.. pascal.caron@univ-rouen.fr, jean-marc.champarnaud@univ-rouen.fr, ludovic.mignot@univ-rouen.fr
Get access

Abstract

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

Keywords

Regular expressionsalternating automataderivationpartial derivation

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. Google Scholar
Antimirov, V.M. and Mosses, P.D., Rewriting extended regular expressions. Theoret. Comput. Sci. 143 (1995) 51–72. Google Scholar
Berry, G. and Sethi, R., From regular expressions to deterministic automata. Theoret. Comput. Sci. 48 (1986) 117–126. Google Scholar
Brzozowski, J.A., Derivatives of regular expressions. J. Assoc. Comput. Mach. 11 (1964) 481–494. Google Scholar
Brzozowski, J.A., Quotient complexity of regular languages. J. Automata, Languages and Combinatorics 15 (2010) 71–89. Google Scholar
Brzozowski, J.A. and Leiss, E.L., On equations for regular languages, finite automata, and sequential networks. Theoret. Comput. Sci. 10 (1980) 19–35. Google Scholar
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.
Champarnaud, J.-M., Ouardi, F. and Ziadi, D., An efficient computation of the equation K-automaton of a regular K-expression. Fundam. Inform. 90 (2009) 1–16. Google Scholar
Champarnaud, J.-M. and Ziadi, D., Canonical derivatives, partial derivatives, and finite automaton constructions. Theoret. Comput. Sci. 239 (2002) 137–163. Google Scholar
J. Clarke, An algorithm for RELAX NG validation. Implementation Report (2002).
J.-H. Conway, Regular algebra and finite machines. Chapman and Hall (1971).
Ginzburg, A., A procedure for checking equality of regular expressions. J. ACM 14 (1967) 355–362. Google Scholar
Ilie, L. and Yu, S., Follow automata. Inf. Comput. 186 (2003) 140–162. Google Scholar
Krob, D., Differentation of K-rational expressions. Internat. J. Algebra Comput. 2 (1992) 57–87. Google Scholar
Lombardy, S. and Sakarovitch, J., Derivatives of rational expressions with multiplicity. Theoret. Comput. Sci. 332 (2005) 141–177. Google Scholar
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.
J. Myhill, Finite automata and the representation of events. WADD TR-57-624 (1957) 112–137.
A. Nerode, Linear automata transformation, in Proc. of AMS 9 (1958) 541–544.
Owens, S., Reppy, J.H. and Turon, A., Regular-expression derivatives re-examined. J. Funct. Program. 19 (2009) 173–190. Google Scholar
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.
M. Sulzmann and K.Z.M. Lu, Partial derivative regular expression pattern matching. Manuscript (2007).
Thompson, K., Regular expression search algorithm. Comm. ACM 11 (1968) 419–422. Google Scholar