Abstract
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.
This work was partially supported by PRIN project Linguaggi Formali e Automi: aspetti matematici e applicativi.
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Giammarresi, D. (2007). Tiling Recognizable Two-Dimensional Languages. In: Bozapalidis, S., Rahonis, G. (eds) Algebraic Informatics. CAI 2007. Lecture Notes in Computer Science, vol 4728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75414-5_5
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DOI: https://doi.org/10.1007/978-3-540-75414-5_5
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