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Combinatorial remarks on two-dimensional Languages

Abstract : The thesis contains a first charter with preliminaries on two-dimensional languages, we give a brief review of the main results and the different characterizations of tiling system recognizable languages which play the central role in the thesis. Then we describe the algebraic structure of the families of local languages. We show that this structure is a lattice with respect to the inclusion and we investigate the properties of the lattice. Moreover we deal with computational problems, studying their decidability and we give the position, in the arithmetical hierarchy, of the classical problems on string languages now turned to two-dimensional languages. In the thesis after some basic definitions concerning polyominoes, we deal with the recognizability of several classes of polyominoes by tiling system recognizable languages. In particular we give the tiling systems for languages representing some classes of convex polyominoes, as the h-convex or parallelogram. Moreover we investigate the recognizability of L-convex polyominoes. Finally, the la test part of the thesis is devoted to the application of tiling system recognizable languages to DNA computation. We give the idea about the construction with DNA of some classes of polyominoes (i.e. the class of parallelogram polyominoes), get through to the family of tiling system recognizable languages.
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Submitted on : Friday, September 11, 2009 - 1:18:16 PM
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  • HAL Id : tel-00415871, version 1



Francesca de Carli. Combinatorial remarks on two-dimensional Languages. Mathematics [math]. Université de Savoie, 2009. English. ⟨tel-00415871⟩



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