Framed versus unframed two-dimensional languages

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. Differently3from 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. © Springer-Verlag Berlin Heidelberg 2009.