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two-dimensional languages.

RAIRO - Theoretical Informatics and Applications (1)

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Unambiguous recognizable two-dimensional languages
Marcella Anselmo, Dora Giammarresi, Maria Madonia, Antonio Restivo
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 40 / Issue 2 / April 2006

Published online by Cambridge University Press:

20 July 2006, pp. 277-293

Print publication:

April 2006
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We consider the family UREC of unambiguous recognizable two-dimensional languages. We prove that there are recognizable languages that are inherently ambiguous, that is UREC family is a proper subclass of REC family. The result is obtained by showing a necessary condition for unambiguous recognizable languages. Further UREC family coincides with the class of picture languages defined by unambiguous 2OTA and it strictly contains its deterministic counterpart. Some closure and non-closure properties of UREC are presented. Finally we show that it is undecidable whether a given tiling system is unambiguous.