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- Title
Recognizability of iso-picture languages by Wang systems.
- Authors
Kalyani, T.; Dare, V. R.; Thomas, D. G.
- Abstract
In 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.,<BIBR>2004</BIBR>]. In [Kalyani et al.,<BIBR>2005</BIBR>], we introduced iso-triangular domino systems (IDS) to recognize iso-picture languages, and proved the equivalence of ITS and IDS. In [Kalyani et al.,<BIBR>2006</BIBR>], 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 systems 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.
- Subjects
PROGRAMMING languages; IDS (Computer program language); TILING (Mathematics); ALGORITHMS; WANG word processors
- Publication
International Journal of Imaging Systems & Technology, 2009, Vol 19, Issue 2, p140
- ISSN
0899-9457
- Publication type
Article
- DOI
10.1002/ima.20185