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Generalized Forbidding Matrix Grammars and Their Membrane Computing Perspective

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Membrane Computing (CMC 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12687))

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Abstract

Matrix grammars are one of the first approaches ever proposed in regulated rewriting, prescribing that rules have to be applied in a certain order. In traditional regulated rewriting, the most interesting case shows up when all rules are context-free. Typical descriptional complexity measures incorporate the number of nonterminals or the length, i.e., the number of rules per matrix. When viewing matrices as program fragments, it becomes natural to consider additional applicability conditions for such matrices. Here, we focus on forbidding sets, i.e., a matrix is applicable to a sentential form w only if none of the words in its forbidding set occurs as a subword in w. This gives rise to further natural descriptional complexity measures: How long could words in forbidding sets be? How many words could be in any forbidding set? How many matrices contain non-empty forbidding contexts? As context-free grammars with forbidding sets are known as generalized forbidding grammars, we call this variant of matrix grammars also generalized forbidding. In this paper, we attempt to answer the above four questions while studying the computational completeness of generalized forbidding matrix grammars. We also link our research to processing strings with membrane computing and discuss appropriate variations of \(\textsf {P}\) systems.

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Notes

  1. 1.

    Notice that computational completeness results have quite some history in the literature of \(\textsf {GF}\) grammars; we only refer to [7, 17,18,19,20] in some historical order. In the long version of [7] which is appearing in Discrete Applied Mathematics [8], we obtained some further improved results of the conference version [7].

  2. 2.

    For the subtle distinction between possibly allowing or disallowing the empty word for v or u, respectively, we refer to the discussions in [7].

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Acknowledgement

Without the numerous contributions of Gheorghe Păun to the theory of Formal Languages, the present paper could hardly be written, as it is based in particular on [12, 22, 23]. Also, the second author profusely thanks Gheorghe Păun for being his source of inspiration since from his Ph.D. days. Happy birthday, Gheorghe!

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Authors and Affiliations

  1. Fachbereich 4 – Abteilung Informatikwissenschaften, Universität Trier, 54286, Trier, Germany

    Henning Fernau

  2. School of Computer Science and Engineering, VIT University, Vellore, 632 014, India

    Lakshmanan Kuppusamy

  3. Department of Applied Mathematics and Computational Sciences, PSG College of Technology, Coimbatore, 641 004, India

    Indhumathi Raman

Authors
  1. Henning Fernau
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  2. Lakshmanan Kuppusamy
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  3. Indhumathi Raman
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Corresponding author

Correspondence to Henning Fernau .

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Editors and Affiliations

  1. TU Wien, Vienna, Austria

    Rudolf Freund

  2. Mongolian University of Science and Technology, Ulaanbaatar, Mongolia

    Tseren-Onolt Ishdorj

  3. Leiden University, Leiden, The Netherlands

    Grzegorz Rozenberg

  4. Turku Center for Computer Science, Turku, Finland

    Arto Salomaa

  5. University of Milano-Bicocca, Milan, Italy

    Claudio Zandron

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Fernau, H., Kuppusamy, L., Raman, I. (2021). Generalized Forbidding Matrix Grammars and Their Membrane Computing Perspective. In: Freund, R., Ishdorj, TO., Rozenberg, G., Salomaa, A., Zandron, C. (eds) Membrane Computing. CMC 2020. Lecture Notes in Computer Science(), vol 12687. Springer, Cham. https://doi.org/10.1007/978-3-030-77102-7_3

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  • DOI: https://doi.org/10.1007/978-3-030-77102-7_3

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