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Efficiency of automata in semi-commutation verification techniques

Published online by Cambridge University Press:  25 September 2007

Gérard Cécé ,
Pierre-Cyrille Héam  and
Yann Mainier
Gérard Cécé
Affiliation:
LIFC, CNRS FRE 2661, Projet INRIA-CASSIS, Université de Franche-Comté, 16 route de Gray, 25030 Besancon Cedex, France; Gerard.Cece@univ-fcomte.fr; Pierre-Cyrille.Heam@univ-fcomte.fr; Yann.Mainier@univ-fcomte.fr
Pierre-Cyrille Héam
Affiliation:
LIFC, CNRS FRE 2661, Projet INRIA-CASSIS, Université de Franche-Comté, 16 route de Gray, 25030 Besancon Cedex, France; Gerard.Cece@univ-fcomte.fr; Pierre-Cyrille.Heam@univ-fcomte.fr; Yann.Mainier@univ-fcomte.fr
Yann Mainier
Affiliation:
LIFC, CNRS FRE 2661, Projet INRIA-CASSIS, Université de Franche-Comté, 16 route de Gray, 25030 Besancon Cedex, France; Gerard.Cece@univ-fcomte.fr; Pierre-Cyrille.Heam@univ-fcomte.fr; Yann.Mainier@univ-fcomte.fr
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Abstract

Computing the image of a regular language by the transitive closure of a relation is a central question in regular model checking. In a recent paper Bouajjani et al. [IEEE Comput. Soc. (2001) 399–408] proved that the class of regular languages L – called APC – of the form UjL0,jL1,jL2,j...Lkj,j, where the union is finite and each Li,j is either a single symbol or a language of the form B* with B a subset of the alphabet, is closed under all semi-commutation relations R. Moreover a recursive algorithm on the regular expressions was given to compute R*(L). This paper provides a new approach, based on automata, for the same problem. Our approach produces a simpler and more efficient algorithm which furthermore works for a larger class of regular languages closed under union, intersection, semi-commutation relations and conjugacy. The existence of this new class, PolC, answers the open question proposed in the paper of Bouajjani et al.

Keywords

Regular model checkingverificationparametric systemssemi-commutations
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 2 , April 2008 , pp. 197 - 215
Copyright
© EDP Sciences, 2007

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