Unambiguous recognizable two-dimensional languages
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 40 (2006) no. 2, p. 277-293

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.

DOI : https://doi.org/10.1051/ita:2006008
Classification:  68Q45,  68Q10
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},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {2},
     year = {2006},
     pages = {277-293},
     doi = {10.1051/ita:2006008},
     zbl = {1112.68085},
     mrnumber = {2252639},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 40 (2006) no. 2, pp. 277-293. doi : 10.1051/ita:2006008. http://www.numdam.org/item/ITA_2006__40_2_277_0/

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