Acta Informatica

, Volume 56, Issue 1, pp 35–59 | Cite as

On path-controlled insertion–deletion systems

  • Henning Fernau
  • Lakshmanan Kuppusamy
  • Indhumathi RamanEmail author
Original Article


A graph-controlled insertion–deletion system is a regulated extension of an insertion–deletion system. It has several components and each component contains some insertion–deletion rules. These components are the vertices of a directed control graph. A transition is performed by any applicable rule in the current component on a string and the resultant string is then moved to the target component specified in the rule. This also describes the arcs of the control graph. Starting from an axiom in the initial component, strings thus move through the control graph. The language of the system is the set of all terminal strings collected in the final component. In this paper, we investigate a variant of the main question in this area: which combinations of size parameters (the maximum number of components, the maximal length of the insertion string, the maximal length of the left context for insertion, the maximal length of the right context for insertion; plus three similar restrictions with respect to deletion) are sufficient to maintain computational completeness of such restricted systems under the additional restriction that the (undirected) control graph is a path? Notice that these results also bear consequences for the domain of insertion–deletion P systems, improving on a number of previous results from the literature, concerning in particular the number of components (membranes) that are necessary for computational completeness results.



Some part of the work done by the second author was during his visit to University of Trier, Germany, in December 2016. The possibility to use some overhead money from the DFG Grant FE 560/6-1 to finance this visit is gratefully acknowledged.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fachbereich 4 – Abteilung Informatikwissenschaften, CIRTUniversität TrierTrierGermany
  2. 2.School of Computer Science and EngineeringVIT UniversityVelloreIndia
  3. 3.School of Information Technology and EngineeringVIT UniversityVelloreIndia

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