Efficiency of Automata in Semi-Commutation Verification Techniques

Gérard Cécé 1, 2 Pierre-Cyrille Héam 1, 2 Yann Mainier 1, 2
1 CASSIS - Combination of approaches to the security of infinite states systems
FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174), INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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, Muscholl and Touili \cite{Anca} proved that the class of regular languages L -- called APC -- of the form of a union of 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, PolC, answers the open question proposed in the paper of Bouajjani and al.
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Gérard Cécé, Pierre-Cyrille Héam, Yann Mainier. Efficiency of Automata in Semi-Commutation Verification Techniques. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), EDP Sciences, 2008, 42 (2), pp.197--215. ⟨10.1051/ita:2007029⟩. ⟨hal-00563430⟩

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