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Computational Completeness of Simple Semi-conditional Insertion-Deletion Systems

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Unconventional Computation and Natural Computation (UCNC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10867))

Abstract

Insertion-deletion (or ins-del for short) systems are well studied in formal language theory, especially regarding their computational completeness. The need for many variants on ins-del systems was raised by the computational completeness result of ins-del system with (optimal) size (1, 1, 1; 1, 1, 1). Several regulations like graph-control, matrix and semi-conditional have been imposed on ins-del systems. Typically, computational completeness are obtained as trade-off results, reducing the size, say, to (1, 1, 0, 1, 1, 0) at the expense of increasing other measures of descriptional complexity. In this paper, we study simple semi-conditional ins-del systems, where an ins-del rule can be applied only in the presence or absence of substrings of the derivation string. We show that simple semi-conditional ins-del system, with maximum permitting string length 2 and maximum forbidden string length 1 and sizes (2, 0, 0; 2, 0, 0), (1, 1, 0; 2, 0, 0), or (1, 1, 0; 1, 1, 1), are computationally complete. We also describe RE by a simple semi-conditional ins-del system of size (1, 1, 0; 1, 1, 0) and with maximum permitting and forbidden string lengths 3 and 1, respectively. The obtained results complement the existing results available in the literature.

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Notes

  1. 1.

    Again, any r4 could be applied, but we will soon see that \(r=p\) is enforced.

  2. 2.

    Again, any r5 could be applied, but we will soon see that \(r=p\) is enforced.

References

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Authors and Affiliations

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

    Henning Fernau, Lakshmanan Kuppusamy & Indhumathi Raman

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

    Henning Fernau, Lakshmanan Kuppusamy & Indhumathi Raman

  3. School of Information Technology and Engineering, VIT, Vellore, 632 014, India

    Henning Fernau, Lakshmanan Kuppusamy & 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 Indhumathi Raman .

Editor information

Editors and Affiliations

  1. University of York, Heslington, York, United Kingdom

    Susan Stepney

  2. Université Paris-Est Créteil, Créteil, France

    Sergey Verlan

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Fernau, H., Kuppusamy, L., Raman, I. (2018). Computational Completeness of Simple Semi-conditional Insertion-Deletion Systems. In: Stepney, S., Verlan, S. (eds) Unconventional Computation and Natural Computation. UCNC 2018. Lecture Notes in Computer Science(), vol 10867. Springer, Cham. https://doi.org/10.1007/978-3-319-92435-9_7

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  • DOI: https://doi.org/10.1007/978-3-319-92435-9_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-92434-2

  • Online ISBN: 978-3-319-92435-9

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