Computational Completeness of Path-Structured Graph-Controlled Insertion-Deletion Systems

  • Henning Fernau
  • Lakshmanan Kuppusamy
  • Indhumathi RamanEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10329)


A graph-controlled insertion-deletion (GCID) 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 rule is applied to a string in a component and the resultant string is moved to the target component specified in the rule, describing the arcs of the control graph. We investigate 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; a similar three restrictions with respect to deletion) are sufficient to maintain the computational completeness of such restricted systems with the additional restriction that the control graph is a path, thus, these results also hold for ins-del P systems.


Graph-controlled ins-del systems Path-structured control graph Computational completeness Descriptional complexity measures 



This work was supported by overhead money from the DFG grant FE 560/6-1.


  1. 1.
    Benne, R. (ed.): RNA Editing: The Alteration of Protein Coding Sequences of RNA. Molecular Biology. Ellis Horwood, Chichester (1993)Google Scholar
  2. 2.
    Fernau, H.: An essay on general grammars. J. Automata Lang. Comb. 21, 69–92 (2016)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Fernau, H., Kuppusamy, L.: Parikh images of matrix ins-del systems. In: Gopal, T.V., Jäger, G., Steila, S. (eds.) TAMC 2017. LNCS, vol. 10185, pp. 201–215. Springer, Cham (2017). doi: 10.1007/978-3-319-55911-7_15 CrossRefGoogle Scholar
  4. 4.
    Fernau, H., Kuppusamy, L., Raman, I.: Generative power of graph-controlled ins-del systems with small sizes. Accepted with J. Automata Lang. Comb. (2017)Google Scholar
  5. 5.
    Fernau, H., Kuppusamy, L., Raman, I.: On the computational completeness of graph-controlled insertion-deletion systems with binary sizes. Accepted with Theor. Comput. Sci. (2017).
  6. 6.
    Freund, R., Kogler, M., Rogozhin, Y., Verlan, S.: Graph-controlled insertion-deletion systems. In: McQuillan, I., Pighizzini, G. (eds.) Proceedings Twelfth Annual Workshop on Descriptional Complexity of Formal Systems, DCFS. EPTCS, vol. 31, pp. 88–98 (2010)Google Scholar
  7. 7.
    Geffert, V.: Normal forms for phrase-structure grammars. RAIRO Informatique Théorique Appl. / Theor. Inf. Appl. 25, 473–498 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Ivanov, S., Verlan, S.: About one-sided one-symbol insertion-deletion P systems. In: Alhazov, A., Cojocaru, S., Gheorghe, M., Rogozhin, Y., Rozenberg, G., Salomaa, A. (eds.) CMC 2013. LNCS, vol. 8340, pp. 225–237. Springer, Heidelberg (2014). doi: 10.1007/978-3-642-54239-8_16 CrossRefGoogle Scholar
  9. 9.
    Kari, L., Thierrin, G.: Contextual insertions/deletions and computability. Inf. Comput. 131(1), 47–61 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Krassovitskiy, A., Rogozhin, Y., Verlan, S.: Further results on insertion-deletion systems with one-sided contexts. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008. LNCS, vol. 5196, pp. 333–344. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-88282-4_31 CrossRefGoogle Scholar
  11. 11.
    Marcus, S.: Contextual grammars. Rev. Roum. Mathématiques Pures Appliquées 14, 1525–1534 (1969)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Matveevici, A., Rogozhin, Y., Verlan, S.: Insertion-deletion systems with one-sided contexts. In: Durand-Lose, J., Margenstern, M. (eds.) MCU 2007. LNCS, vol. 4664, pp. 205–217. Springer, Heidelberg (2007). doi: 10.1007/978-3-540-74593-8_18 CrossRefGoogle Scholar
  13. 13.
    Păun, Gh.: Membrane Computing: An Introduction. Springer, Heidelberg (2002)Google Scholar
  14. 14.
    Păun, Gh., Rozenberg, G., Salomaa, A.: DNA Computing: New Computing Paradigms. Springer, Heidelberg (1998)Google Scholar
  15. 15.
    Takahara, A., Yokomori, T.: On the computational power of insertion-deletion systems. Nat. Comput. 2(4), 321–336 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Verlan, S.: Recent developments on insertion-deletion systems. Comput. Sci. J. Moldova 18(2), 210–245 (2010)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Henning Fernau
    • 1
  • Lakshmanan Kuppusamy
    • 2
  • Indhumathi Raman
    • 3
    Email author
  1. 1.Fachbereich 4 – CIRTUniversität TrierTrierGermany
  2. 2.SCOPEVIT UniversityVelloreIndia
  3. 3.SITEVIT UniversityVelloreIndia

Personalised recommendations