On the Tiling System Recognizability of Various Classes of Convex Polyominoes

We consider some problems concerning two relevant classes of two-dimensional languages, i.e., the tiling recognizable languages, and the local languages, recently introduced by Giammarresi and Restivo and already extensively studied. We show that various classes of convex and column-convex polyominoes can be naturally represented as two-dimensional words of tiling recognizable languages. Moreover, we investigate the nature of the generating function of a tiling recognizable language, providing evidence that such a generating function need not be D-finite.