# 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

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topCécé, 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 -

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