Recognizability of iso‐picture languages by Wang systems

Abstract

AbstractIn the context of a syntactic approach to pattern recognition, there have been several studies in the last few decades ontheoretical models for generating or recognizing two‐dimensional objects, pictures, and picture languages. Motivated by these studies, we have introduced a new notion of recognizability for a class of picture languages called iso‐picture languages through iso‐triangular tiling systems (ITS) and studied the properties of these languages [Kalyani et al.,2004]. In [Kalyani et al.,2005], we introduced iso‐triangular domino systems (IDS) to recognize iso‐picture languages, and proved the equivalence of ITS and IDS. In [Kalyani et al.,2006], we have constructed a two‐dimensional online tessellation automaton (IPOTA) to recognize an iso‐picture language and presented an algorithm to learn recognizable iso‐picture languages from positive data and restricted subset queries. In this article, we introduce iso‐triangular Wang systems (IWS) to recognize iso‐picture languages. We prove that the family of iso‐picture languages recognized by iso‐triangular Wang systems ℒ(IWS) coincides with the family of iso‐picture languages recognized by iso‐triangular tiling sytems ℒ(ITS). We show that ℒ(ITS) = ℒ(IDS) as a corollary and obtain that the families of iso‐picture languages ℒ(ITS), ℒ(IDS), ℒ(IWS), and ℒ(IPOTA) all coincide. © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 140–145, 2009.