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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 ${\cup }_j$ $L_{0,j}$ $L_{1,j}$ $L_{2,j}$ $...$ $L_{k_j,j}$, 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...

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 [ (2001) 399–408] proved that the class of regular languages – called APC – of the form U ..., where the union is finite and each is either a single symbol or a language of the form with a subset of the alphabet, is closed under all semi-commutation relations . Moreover a recursive...