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Universal Matrix Insertion Grammars with Small Size

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Unconventional Computation and Natural Computation (UCNC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10240))

Abstract

We study matrix insertion grammars (MIS) towards representation of recursively enumerable languages with small size. We show that pure MIS of size (3; 1, 2, 2) (i.e., having ternary matrices inserting one symbol in two symbol context) can characterize all recursively enumerable languages. This is achieved by either applying an inverse morphism and a weak coding, or a left (right) quotient with a regular language or an intersection with a regular language followed by a weak coding. The obtained results complete known results on insertion-deletion systems from DNA computing area.

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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. Laboratoire d’Algorithmique, Complexité et Logique, Université Paris Est - Créteil Val de Marne, 94010, Créteil, France

    Sergey Verlan

Authors
  1. Henning Fernau
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  2. Lakshmanan Kuppusamy
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  3. Sergey Verlan
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Corresponding author

Correspondence to Sergey Verlan .

Editor information

Editors and Affiliations

  1. University of Arkansas, Fayetteville, Arkansas, USA

    Matthew J. Patitz

  2. University of Sheffield, Sheffield, United Kingdom

    Mike Stannett

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Fernau, H., Kuppusamy, L., Verlan, S. (2017). Universal Matrix Insertion Grammars with Small Size. In: Patitz, M., Stannett, M. (eds) Unconventional Computation and Natural Computation. UCNC 2017. Lecture Notes in Computer Science(), vol 10240. Springer, Cham. https://doi.org/10.1007/978-3-319-58187-3_14

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  • DOI: https://doi.org/10.1007/978-3-319-58187-3_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58186-6

  • Online ISBN: 978-3-319-58187-3

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