Efficiency of automata in semi-commutation verification techniques

Cécé, Gérard ; Héam, Pierre-Cyrille ; Mainier, Yann

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008), p. 197-215 / Harvested from Numdam

Résumé

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.

Détail

Publié le : 2008-01-01

MR 2401258 | Zbl 1144.68039

DOI : https://doi.org/10.1051/ita:2007029
Classification:  68N30

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