On the Nonterminal Complexity of Tree Controlled Grammars

  • György Vaszil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7300)


A tree controlled grammar is a regulated rewriting device which can be given as a pair (G,R) where G is a context-free grammar and R is a regular set over the terminal and nonterminal alphabets of G. The language generated by the tree controlled grammar contains those words of L(G) which have a derivation tree where all the words obtained by reading the symbols labeling the nodes belonging to the different levels of the tree, from left to right, belong to the language R. The nonterminal complexity of tree controlled grammars can be given as the number of nonterminals of the context-free grammar G, and the number of nonterminals that a regular grammar needs to generate the control language R. Here we improve the currently known best upper bound on the nonterminal complexity of tree controlled grammars from seven to six, that is, we show that a context-free grammar with five nonterminals and a control language which can be generated by a grammar with one nonterminal is sufficient to generate any recursively enumerable language.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Čulik II, K., Maurer, H.: Tree controlled grammars. Computing 19, 129–139 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. Springer, Berlin (1989)CrossRefzbMATHGoogle Scholar
  3. 3.
    Dassow, J., Păun, G., Salomaa, A.: Grammars with controlled derivations. In: Salomaa, A., Rozenberg, G. (eds.) Handbook of Formal Languages, vol. II, pp. 101–154. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  4. 4.
    Dassow, J., Stiebe, R., Truthe, B.: Generative capacity of subregularly tree controlled grammars. International Journal of Foundations of Computer Science 21 (2010)Google Scholar
  5. 5.
    Frisco, P.: Computing with Cells. Advances in Membrane Computing. Oxford University Press, New York (2009)CrossRefzbMATHGoogle Scholar
  6. 6.
    Geffert, V.: Context-Free-Like Forms for the Phrase Structure Grammars. In: Chytil, M.P., Janiga, L., Koubek, V. (eds.) MFCS 1988. LNCS, vol. 324, pp. 309–317. Springer, Heidelberg (1988)CrossRefGoogle Scholar
  7. 7.
    Păun, G.: On the generative capacity of tree controlled grammars. Computing 21, 213–220 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Springer, Berlin (1997)zbMATHGoogle Scholar
  9. 9.
    Salomaa, A.: Formal Languages. Academic Press, New York (1973)zbMATHGoogle Scholar
  10. 10.
    Turaev, S., Dassow, J., Selamat, M.: Language Classes Generated by Tree Controlled Grammars with Bounded Nonterminal Complexity. In: Holzer, M., Kutrib, M., Pighizzini, G. (eds.) DCFS 2011. LNCS, vol. 6808, pp. 289–300. Springer, Heidelberg (2011)Google Scholar
  11. 11.
    Turaev, S., Dassow, J., Selamat, M.: Nonterminal complexity of tree controlled grammars. Theoretical Computer Science 412(41), 5789–5795 (2011)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • György Vaszil
    • 1
  1. 1.Department of Computer Science, Faculty of InformaticsUniversity of DebrecenDebrecenHungary

Personalised recommendations