Monadic second-order logic over rectangular pictures and recognizability by tiling systems
Information and Computation
Handbook of formal languages, vol. 3
Automata, Languages, and Machines
Automata, Languages, and Machines
On Some Recognizable Picture-Languages
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
A Characterization of Recognizable Picture Languages
ICPIA '92 Proceedings of the Second International Conference on Parallel Image Analysis
Regular Expressions and Context-Free Grammars for Picture Languages
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
On Piecewise Testable, Starfree, and Recognizable Picture Languages
FoSSaCS '98 Proceedings of the First International Conference on Foundations of Software Science and Computation Structure
The Monadic Quantifier Alternation Hierarchy over Graphs is Infinite
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
New operations and regular expressions for two-dimensional languages over one-letter alphabet
Theoretical Computer Science - The art of theory
Automata on a 2-dimensional tape
FOCS '67 Proceedings of the 8th Annual Symposium on Switching and Automata Theory (SWAT 1967)
From determinism to non-determinism in recognizable two-dimensional languages
DLT'07 Proceedings of the 11th international conference on Developments in language theory
Tiling automaton: a computational model for recognizable two-dimensional languages
CIAA'07 Proceedings of the 12th international conference on Implementation and application of automata
Deterministic two-dimensional languages over one-letter alphabet
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
Picture Languages: From Wang Tiles to 2D Grammars
CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
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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.