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Unambiguous recognizable two-dimensional languages

Published online by Cambridge University Press:  20 July 2006

Marcella Anselmo ,
Dora Giammarresi ,
Maria Madonia  and
Antonio Restivo
Marcella Anselmo
Affiliation:
Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84081 Baronissi, (Salerno), Italy; anselmo@dia.unisa.it
Dora Giammarresi
Affiliation:
Dipartimento di Matematica, Università di Roma “Tor Vergata”, via Ricerca Scientifica, 00133 Roma, Italy; giammarr@mat.uniroma2.it
Maria Madonia
Affiliation:
Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria 6/a, 95125 Catania, Italy; madonia@dmi.unict.it
Antonio Restivo
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Palermo, via Archirafi 34, 90123 Palermo, Italy; restivo@dipmat.math.unipa.it
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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.

Keywords

Automata and formal languagesunambiguitydeterminismtwo-dimensional languages.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 40 , Issue 2: Alberto Bertoni: Climbing summits , April 2006 , pp. 277 - 293
Copyright
© EDP Sciences, 2006

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