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.
Keywords: automata and formal languages, unambiguity, determinism, two-dimensional languages
@article{ITA_2006__40_2_277_0,
author = {Anselmo, Marcella and Giammarresi, Dora and Madonia, Maria and Restivo, Antonio},
title = {Unambiguous recognizable two-dimensional languages},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {277--293},
year = {2006},
publisher = {EDP Sciences},
volume = {40},
number = {2},
doi = {10.1051/ita:2006008},
mrnumber = {2252639},
zbl = {1112.68085},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ita:2006008/}
}
TY - JOUR AU - Anselmo, Marcella AU - Giammarresi, Dora AU - Madonia, Maria AU - Restivo, Antonio TI - Unambiguous recognizable two-dimensional languages JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2006 SP - 277 EP - 293 VL - 40 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ita:2006008/ DO - 10.1051/ita:2006008 LA - en ID - ITA_2006__40_2_277_0 ER -
%0 Journal Article %A Anselmo, Marcella %A Giammarresi, Dora %A Madonia, Maria %A Restivo, Antonio %T Unambiguous recognizable two-dimensional languages %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2006 %P 277-293 %V 40 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ita:2006008/ %R 10.1051/ita:2006008 %G en %F ITA_2006__40_2_277_0
Anselmo, Marcella; Giammarresi, Dora; Madonia, Maria; Restivo, Antonio. Unambiguous recognizable two-dimensional languages. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 2, pp. 277-293. doi: 10.1051/ita:2006008
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