Tiling Recognizable Two-Dimensional Languages

  • Dora Giammarresi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4728)


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.


Automata and Formal Languages Two-dimensional languages Tiling systems Unambiguity Determinism 


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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Dora Giammarresi
    • 1
  1. 1.Dipartimento di Matematica. Università di Roma “Tor Vergata”, via della Ricerca Scientifica, 00133 RomaItaly

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