k-Local Internal Contextual Grammars

  • Radu Gramatovici
  • Florin Manea
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6808)

Abstract

In this paper we propose a generalization of the local internal contextual grammars, introduced by Ilie in 1997, namely the k-local internal contextual grammars. These grammars are, in fact, classical internal contextual grammars, but their only permitted derivations are those that can be described in a restricted manner (that depends on the number k). Using this formalism we define different classes of languages, and obtain a series of language theoretic results for them. Also, we show that the membership problem for k-local internal contextual grammars with polynomial choice can be solved in polynomial time. This seems interesting to us, as it shows that the descriptional restrictions on the derivations of a grammar reflect on the computational efficiency of accepting the language generated by that grammar.

Keywords

Internal contextual grammars k-Local Derivation Hierarchy of languages Membership problem 

References

  1. 1.
    Marcus, S.: Contextual grammars. Revue Roum. Math. Pures Appl. 14, 1525–1534 (1969)MATHMathSciNetGoogle Scholar
  2. 2.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Springer, Berlin (1997)MATHGoogle Scholar
  3. 3.
    Păun, G.: Marcus Contextual Grammars. Kluwer Publ. House, Dordrecht (1998)MATHGoogle Scholar
  4. 4.
    Gramatovici, R., Martín-Vide, C.: Sorted dependency insertion grammars. Theor. Comput. Sci. 354(1), 142–152 (2006)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Gramatovici, R.: An efficient parser for a class of contextual languages. Fundam. Inform. 33, 211–238 (1998)MATHMathSciNetGoogle Scholar
  6. 6.
    Enguix, G.B., Gramatovici, R.: Parsing with active p automata. In: Martín-Vide, C., Mauri, G., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2003. LNCS, vol. 2933, pp. 31–42. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Gramatovici, R., Manea, F.: Parsing local internal contextual languages with context-free choice. Fundam. Inform. 64, 171–183 (2005)MATHMathSciNetGoogle Scholar
  8. 8.
    Gramatovici, R., Manea, F.: A cyk-based parser for local internal contextual grammars with context-free choice. In: Proc. AFL 2005, pp. 31–42 (2005)Google Scholar
  9. 9.
    Harbusch, K.: An efficient online parser for contextual grammars with at most context-free selectors. In: Gelbukh, A. (ed.) CICLing 2003. LNCS, vol. 2588, pp. 168–179. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  10. 10.
    Harbusch, K.: Parsing contextual grammars with linear, regular and context-free selectors. In: Grammars and Automata for String Processing. Topics in Computer Mathematics, vol. 9, pp. 45–54. Taylor and Francis, Abington (2003)CrossRefGoogle Scholar
  11. 11.
    Jancar, P., Mráz, F., Plátek, M., Procházka, M., Vogel, J.: Restarting automata, marcus grammars and context-free languages. Developments in Language Theory, 102–111 (1995)Google Scholar
  12. 12.
    Mráz, F., Plátek, M., Procházka, M.: Restarting automata, deleting and marcus grammars. In: Recent Topics in Mathematical and Computational Linguistics, pp. 218–233. Romanian Academy Publishing House (2000)Google Scholar
  13. 13.
    Ilie, L.: On computational complexity of contextual languages. Theor. Comput. Sci. 183(1), 33–44 (1997)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Gramatovici, R., Manea, F.: k-Local Internal Contextual Grammars. Technical report, Otto-von-Guericke-Universität Magdeburg, Fakultät für Informatik (2011), http://theo.cs.uni-magdeburg.de/pubs/preprints/pp-afl-2011-06.pdf

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Radu Gramatovici
    • 1
  • Florin Manea
    • 1
    • 2
  1. 1.Faculty of Mathematics and Computer ScienceUniversity of BucharestBucharestRomania
  2. 2.Fakultät für Informatik PSF 4120Otto-von-Guericke-Universität MagdeburgMagdeburgGermany

Personalised recommendations