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Recognizable Picture Languages and Polyominoes

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Algebraic Informatics (CAI 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4728))

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Abstract

We consider the problem of recognizability of some classes of polyominoes in the theory of picture languages. In particular we focus our attention on the problem posed by Matz of finding a non-recognizable picture language for which his technique for proving the non-recognizability of picture languages fails. We face the problem by studying the family of L-convex polyominoes and some closed families that are similar to the recognizable family of all polyominoes but result to be non-recognizable. Furthermore we prove that the family of L-convex polyominoes satisfies the necessary condition given by Matz for the recognizability and we conjecture that the family of L-convex polyominoes is non-recognizable.

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Authors and Affiliations

  1. Università di Palermo, Dipartimento di Matematica e Applicazioni, via Archirafi, 34 - 90123 Palermo, Italy

    Giusi Castiglione & Roberto Vaglica

Authors
  1. Giusi Castiglione
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  2. Roberto Vaglica
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Symeon Bozapalidis George Rahonis

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Castiglione, G., Vaglica, R. (2007). Recognizable Picture Languages and Polyominoes. In: Bozapalidis, S., Rahonis, G. (eds) Algebraic Informatics. CAI 2007. Lecture Notes in Computer Science, vol 4728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75414-5_10

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  • DOI: https://doi.org/10.1007/978-3-540-75414-5_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75413-8

  • Online ISBN: 978-3-540-75414-5

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