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Computational Completeness of Simple Semi-conditional Insertion-Deletion Systems

  • Henning Fernau
  • Lakshmanan Kuppusamy
  • Indhumathi Raman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Henning Fernau
    • 1
    • 2
    • 3
  • Lakshmanan Kuppusamy
    • 1
    • 2
    • 3
  • Indhumathi Raman
    • 1
    • 2
    • 3
  1. 1.Fachbereich 4 – Abteilung Informatikwissenschaften, CIRTUniversität TrierTrierGermany
  2. 2.School of Computer Science and EngineeringVITVelloreIndia
  3. 3.School of Information Technology and EngineeringVITVelloreIndia

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