Tiling recognizable two-dimensional languages generalizes recognizable string languages to two dimensions and share with them several properties. Nevertheless two-dimensional recognizable languages are not closed under complement and this implies that are intrinsically non-deterministic. We introduce the notion of deterministic and unambiguous tiling system that generalizes deterministic and unambiguous automata for strings and show that, differently from the one-dimensional case, there exist other distinct classes besides deterministic, unambiguous and non-deterministic families that can be separated by means of examples and decidability properties. Finally we introduce a model of automaton, referred to as tiling automaton, defined as a scanning strategy plus a transition function given by a tiling system. Languages recognized by tiling automata are compared with ones recognized by on-line tesselation automata and four-way automata. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Giammarresi, D. (2007). Tiling recognizable two-dimensional languages. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4728 LNCS, pp. 75–86). Springer Verlag. https://doi.org/10.1007/978-3-540-75414-5_5
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