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Parallel Contextual Array Insertion Deletion Grammar and (Context-Free : Context-Free) Matrix Grammar

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Combinatorial Image Analysis (IWCIA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 12148))

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Abstract

Siromoney et al. introduced Siromoney matrix grammars (1973) which are of sequential-parallel type in the sense that first a horizontal string of nonterminals is derived sequentially by applying the horizontal production rules and then vertical productions are applied in parallel to get the intended two-dimensional picture. In 1999, Radhakrishnan et al. introduced and studied a variant of Siromoney matrix grammars called (X:Y)MG where \(X, Y \in \{Context-Free (CF), Regular(R)\}\). James et al. in 2018 introduced Parallel Contextual Array Insertion Deletion Grammar (PCAIDG) to generate two-dimensional array languages using insertion and deletion operations and parallel contextual mappings. In this paper, we prove that this family of languages generated by PCAIDGs properly includes the family (CF : CF) ML.

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Acknowledgment

We are grateful to the reviewers whose comments made to refine the paper significantly.

Author information

Authors and Affiliations

  1. Department of Mathematics, Ramakrishna Mission Vivekananda College, Chennai, 600004, India

    S. Jayasankar

  2. Department of Science and Humanities (Mathematics Division), Saveetha School of Engineering, Chennai, 602 105, India

    D. G. Thomas & S. James Immanuel

  3. Department of Computer Science, University of Trier, Trier, Germany

    Meenakshi Paramasivan

  4. Department of Mathematics, Madras Christian College, Chennai, 600 059, India

    T. Robinson

  5. Department of Mathematics and Computer Science, Liverpool Hope University, Liverpool, L16 9JD, UK

    Atulya K. Nagar

Authors
  1. S. Jayasankar
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  2. D. G. Thomas
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  3. S. James Immanuel
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  4. Meenakshi Paramasivan
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  5. T. Robinson
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  6. Atulya K. Nagar
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Corresponding author

Correspondence to S. Jayasankar .

Editor information

Editors and Affiliations

  1. Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia

    Tibor Lukić

  2. School of Business, SUNY Fredonia, Fredonia, NY, USA

    Reneta P. Barneva

  3. SUNY Buffalo State, Buffalo, NY, USA

    Valentin E. Brimkov

  4. Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia

    Lidija Čomić

  5. Department of Information Technology, Uppsala University, Uppsala, Sweden

    Nataša Sladoje

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Jayasankar, S., Thomas, D.G., Immanuel, S.J., Paramasivan, M., Robinson, T., Nagar, A.K. (2020). Parallel Contextual Array Insertion Deletion Grammar and (Context-Free : Context-Free) Matrix Grammar. In: Lukić, T., Barneva, R., Brimkov, V., Čomić, L., Sladoje, N. (eds) Combinatorial Image Analysis. IWCIA 2020. Lecture Notes in Computer Science(), vol 12148. Springer, Cham. https://doi.org/10.1007/978-3-030-51002-2_11

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  • DOI: https://doi.org/10.1007/978-3-030-51002-2_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-51001-5

  • Online ISBN: 978-3-030-51002-2

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