Framed Versus Unframed Two-Dimensional Languages

Authors:
Marcella Anselmo;Natasha Jonoska;Maria Madonia
Affiliations:
Dipartimento di Informatica ed Applicazioni, Università di Salerno I-84084 Fisciano (SA), Italy;Department of Mathematics and Statistics, University of South Florida, Tampa, USA FL 33620;Dip. Matematica e Informatica, Università di Catania, Catania, Italy 95125
Venue:
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Year:
2009

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Abstract

In this paper we study a class of factor-closed tiling recognizable languages (FREC) that corresponds to certain symbolic dynamical systems called sofic subshifts. This class of languages is a subclass of the two-dimensional class of tiling recognizable languages, denoted REC. Differently from REC, languages in FREC can be recognized without framing pictures with a special boundary symbol. We study (un)ambiguity properties of FREC in comparison to the ones in REC. We show that a frame surrounding each block provides additional memory that can enforce the size and the content of pictures and can change (un)ambiguity properties. Consequently, we propose several variations of "unambiguity" for languages in FREC which may be better suited to understand this class.