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2D Oxide Picture Languages and Their Properties

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Combinatorial Image Analysis (IWCIA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13348))

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Abstract

In the theory of formal languages, two-dimensional (picture) languages are a generalization of string languages to two dimensions. Pictures may be regarded as digitized finite arrays, occurring in studies concerning pattern recognition, image analysis, cellular automata, and parallel computing. Several studies have been done for generating and (or) recognizing rectangular, triangular, and hexagonal arrays using formal syntactic methods. Motivated by oxide molecular structures, the oxide pictures, a special class of two-dimensional pictures, are considered. Various generating and recognizing schemes, such as the Oxide Tiling System (OXTS), Oxide Wang System (OXWS), Oxide Tile Rewriting Grammar (OXTRG), and Oxide Sgraffito Automata (OXS), have been developed recently. It is found that the family of oxide picture languages recognizable by oxide tiling systems is closed under union, overlapping, half-turn, transpose, anti-transpose, and reflection (both along horizontal and vertical lines), but not closed under quarter-turn and anti-quarter-turn. This paper further discusses some language theoretic results as well.

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Acknowledgements

The authors are grateful to the referees for their very useful comments, which helped to improve the presentation of the paper. The third author would like to express gratitude to the University of Trier, Germany, and Madras Christian College in Chennai, India, for visits in 2019 and 2020.

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Authors and Affiliations

  1. Department of Mathematics, Rajalakshmi Engineering College, Chennai, 602105, India

    Helen Vijitha Ponraj

  2. Department of Mathematics, Madras Christian College, Chennai, 600059, India

    Robinson Thamburaj

  3. FB IV - Informatikwissenschaften, Universität Trier, 54286, Trier, Germany

    Meenakshi Paramasivan

Authors
  1. Helen Vijitha Ponraj
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  2. Robinson Thamburaj
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  3. Meenakshi Paramasivan
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Corresponding authors

Correspondence to Helen Vijitha Ponraj , Robinson Thamburaj or Meenakshi Paramasivan .

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Editors and Affiliations

  1. State University of New York at Fredonia, Fredonia, NY, USA

    Reneta P. Barneva

  2. SUNY Buffalo State College, Buffalo, NY, USA

    Valentin E. Brimkov

  3. University of Messina, Messina, Italy

    Giorgio Nordo

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Ponraj, H.V., Thamburaj, R., Paramasivan, M. (2023). 2D Oxide Picture Languages and Their Properties. In: Barneva, R.P., Brimkov, V.E., Nordo, G. (eds) Combinatorial Image Analysis. IWCIA 2022. Lecture Notes in Computer Science, vol 13348. Springer, Cham. https://doi.org/10.1007/978-3-031-23612-9_13

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  • DOI: https://doi.org/10.1007/978-3-031-23612-9_13

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