Efficiency of automata in semi-commutation verification techniques
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 2, pp. 197-215.

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}$${L}_{2,j}$$...$${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 ${R}^{*}\left(L\right)$. 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.

DOI : https://doi.org/10.1051/ita:2007029
Classification : 68N30
Mots clés : regular model checking, verification, parametric systems, semi-commutations
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Cécé, Gérard; Héam, Pierre-Cyrille; Mainier, Yann. Efficiency of automata in semi-commutation verification techniques. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 2, pp. 197-215. doi : 10.1051/ita:2007029. http://www.numdam.org/articles/10.1051/ita:2007029/

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