Efficiency of automata in semi-commutation verification techniques

Gérard Cécé; Pierre-Cyrille Héam; Yann Mainier

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2008)

  • Volume: 42, Issue: 2, page 197-215
  • ISSN: 0988-3754

Abstract

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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 j L 0 , j L 1 , j L 2 , j ... L k j , j , where the union is finite and each L i , 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, Pol 𝒞 , answers the open question proposed in the paper of Bouajjani et al.

How to cite

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Cécé, Gérard, Héam, Pierre-Cyrille, and Mainier, Yann. "Efficiency of automata in semi-commutation verification techniques." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 42.2 (2008): 197-215. <http://eudml.org/doc/245200>.

@article{Cécé2008,
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 $\cup _j$$L_\{0,j\}$$L_\{1,j\}$$L_\{2,j\}$$\ldots $$ L_\{k_j,j\}$, where the union is finite and each $L_\{i,j\}$ 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, Pol$\mathcal \{C\}$, answers the open question proposed in the paper of Bouajjani et al.},
author = {Cécé, Gérard, Héam, Pierre-Cyrille, Mainier, Yann},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {regular model checking; verification; parametric systems; semi-commutations; image of a regular language; transitive closure; model checking},
language = {eng},
number = {2},
pages = {197-215},
publisher = {EDP-Sciences},
title = {Efficiency of automata in semi-commutation verification techniques},
url = {http://eudml.org/doc/245200},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Cécé, Gérard
AU - Héam, Pierre-Cyrille
AU - Mainier, Yann
TI - Efficiency of automata in semi-commutation verification techniques
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2008
PB - EDP-Sciences
VL - 42
IS - 2
SP - 197
EP - 215
AB - 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 $\cup _j$$L_{0,j}$$L_{1,j}$$L_{2,j}$$\ldots $$ L_{k_j,j}$, where the union is finite and each $L_{i,j}$ 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, Pol$\mathcal {C}$, answers the open question proposed in the paper of Bouajjani et al.
LA - eng
KW - regular model checking; verification; parametric systems; semi-commutations; image of a regular language; transitive closure; model checking
UR - http://eudml.org/doc/245200
ER -

References

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