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Two-Dimensional Palindromes and Their Properties

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Language and Automata Theory and Applications (LATA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10168))

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Abstract

A two-dimensional word (2D) is a rectangular finite array of letters from the alphabet \(\varSigma \). A 2D word is said to be a 2D palindrome if it is equal to its reverse image. In this paper, we study some combinatorial properties of 2D palindromes. In particular, we provide a sufficient condition under which a 2D word is said to be a 2D palindrome, discuss the necessary and sufficient condition under which a 2D word can be decomposed into 2D palindromes, and find the relation between the set of all 2D palindromes and the set of all 2D primitive words. We also show that the set of all 2D palindromes is not a recognizable language, and study a special class of 2D palindromes, namely 2D palindrome square words.

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Authors and Affiliations

  1. Department of Mathematics Indian Institute of Technology Madras, Chennai, 600036, India

    Manasi S. Kulkarni & Kalpana Mahalingam

Authors
  1. Manasi S. Kulkarni
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  2. Kalpana Mahalingam
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Corresponding author

Correspondence to Manasi S. Kulkarni .

Editor information

Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Frank Drewes

  2. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  3. University of Giessen, Giessen, Germany

    Bianca Truthe

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Kulkarni, M.S., Mahalingam, K. (2017). Two-Dimensional Palindromes and Their Properties. In: Drewes, F., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2017. Lecture Notes in Computer Science(), vol 10168. Springer, Cham. https://doi.org/10.1007/978-3-319-53733-7_11

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  • DOI: https://doi.org/10.1007/978-3-319-53733-7_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53732-0

  • Online ISBN: 978-3-319-53733-7

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