Picture Recognizability with Automata Based on Wang Tiles

  • Violetta Lonati
  • Matteo Pradella
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5901)

Abstract

We introduce a model of automaton for picture language recognition which is based on tiles and is called Wang automaton, since its description relies on the notation of Wang systems. Wang automata combine features of both online tessellation acceptors and 4-ways automata: as in online tessellation acceptors, computation assigns states to each picture position; as in 4-way automata, the input head visits the picture moving from one pixel to an adjacent one, according to some scanning strategy. We prove that Wang automata recognize the class REC, i.e. they are equivalent to tiling systems or online tessellation acceptors, and hence strictly more powerful than 4-way automata. We also consider a very natural notion of determinism for Wang automata, and study the resulting class, comparing it with other deterministic classes considered in the literature, like DREC and Snake-DREC.

Keywords

Picture languages 2D languages tiling systems 4-way automata online tessellation acceptors Wang systems determinism 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Violetta Lonati
    • 1
  • Matteo Pradella
    • 2
  1. 1.Dipartimento di Scienze dell’InformazioneUniversità degli Studi di MilanoMilanoItaly
  2. 2.IEIIT, Consiglio Nazionale delle RicercheMilanoItaly

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