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On Matrix Ins-Del Systems of Small Sum-Norm

  • Henning FernauEmail author
  • Lakshmanan Kuppusamy
  • Indhumathi Raman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11376)

Abstract

A matrix ins-del system is described by a set of insertion-deletion rules presented in matrix form, which demands all rules of a matrix to be applied in the given order. These systems were introduced to model very simplistic fragments of sequential programs based on insertion and deletion as elementary operations as can be found in biocomputing. We are investigating such systems with limited resources as formalized in descriptional complexity. A traditional descriptional complexity measure of such a system is its ins-del size. Summing up the according numbers, we arrive at the sum-norm. We show that matrix ins-del systems with sum-norm 4 and (i) maximum length 3 with only one of insertion or deletion being performed under a one-sided context, or (ii) maximum length 2 with both insertion and deletion being performed under a one-sided context, can describe all recursively enumerable languages. We also show that if a matrix ins-del system of size s can describe the class of linear languages \(\mathrm {LIN}\), then without any additional resources, matrix ins-del systems of size s also describe the regular closure of \(\mathrm {LIN}\).

Keywords

Matrix ins-del systems Computational completeness Regular closure of linear languages 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Henning Fernau
    • 1
    Email author
  • Lakshmanan Kuppusamy
    • 2
  • Indhumathi Raman
    • 3
  1. 1.Fachbereich 4 - Abteilung Informatikwissenschaften, CIRTUniversität TrierTrierGermany
  2. 2.School of Computer Science and EngineeringVITVelloreIndia
  3. 3.Department of Applied Mathematics and Computational SciencesPSG College of TechnologyCoimbatoreIndia

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