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Issue RAIRO-Theor. Inf. Appl.
Volume 40, Number 2, April-June 2006
Alberto Bertoni: Climbing summits
Page(s) 277 - 293
DOI 10.1051/ita:2006008
Published online 20 July 2006

Theoret. Informatics Appl. 40, 277-293 (2006)
DOI: 10.1051/ita:2006008

Unambiguous recognizable two-dimensional languages

Marcella Anselmo1, Dora Giammarresi2, Maria Madonia3 and Antonio Restivo4

1  Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84081 Baronissi, (Salerno), Italy; anselmo@dia.unisa.it
2  Dipartimento di Matematica, Università di Roma "Tor Vergata", via Ricerca Scientifica, 00133 Roma, Italy; giammarr@mat.uniroma2.it
3  Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria 6/a, 95125 Catania, Italy; madonia@dmi.unict.it
4  Dipartimento di Matematica e Applicazioni, Università di Palermo, via Archirafi 34, 90123 Palermo, Italy; restivo@dipmat.math.unipa.it


(Published online 20 July 2006)

Abstract
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.


Mathematics Subject Classification. 68Q45, 68Q10

Key words: Automata and formal languages -- unambiguity -- determinism -- two-dimensional languages.


© EDP Sciences 2006


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