Advertisement

Cooperating Distributed Grammar Systems: Components with Nonincreasing Competence

  • Maurice H. ter Beek
  • Erzsébet Csuhaj-Varjú
  • Markus Holzer
  • György Vaszil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6610)

Abstract

We study the generative power of CD grammar systems (CDGSs) that use a cooperation protocol based on the level of competence on a sentential form — and the competence of their components does not increase during rewriting. A component of a CDGS is k-competent on a sentential form if it can rewrite exactly k different nonterminals appearing in that string. A CDGS with components that are nonincreasing in competence works in =k-competence mode of derivation if no k-competent component can ever become l-competent, for some l > k. We introduce a static and a dynamic definition to impose this restriction, and we relate the generative power of such CDGSs working either in a sequential or in a parallel manner and according to the aforementioned cooperation protocol, for various k, with that of context-free forbidding random context grammars, (random context) ET0L systems, and context-free programmed grammars with appearance checking.

Keywords

Sentential Form Successful Derivation Dynamic Sense Formal Language Theory Cooperation Protocol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Meersman, R., Rozenberg, G.: Cooperating Grammar Systems. In: Winkowski, J. (ed.) MFCS 1978. LNCS, vol. 64, pp. 364–374. Springer, Heidelberg (1978)CrossRefGoogle Scholar
  2. 2.
    Csuhaj–Varjú, E., Dassow, J.: On Cooperating Distributed Grammar Systems. Journal of Information Processing and Cybernetics EIK 26, 49–63 (1990)zbMATHGoogle Scholar
  3. 3.
    Csuhaj–Varjú, E., Dassow, J., Kelemen, J., Păun, G.: Grammar Systems: A Grammatical Approach to Distribution and Cooperation. Topics in Computer Mathematics, vol. 5. Gordon and Breach, London (1994)zbMATHGoogle Scholar
  4. 4.
    Dassow, J., Păun, G., Rozenberg, G.: Grammar Systems. In: [13], vol. 2, ch. 4, pp. 155–213 (1997)Google Scholar
  5. 5.
    Bordihn, H., Csuhaj–Varjú, E.: On Competence and Completeness in CD Grammar Systems. Acta Cybernetica 12, 347–361 (1996)MathSciNetzbMATHGoogle Scholar
  6. 6.
    ter Beek, M.H., Csuhaj–Varjú, E., Holzer, M., Vaszil, G.: On Competence in CD Grammar Systems. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds.) DLT 2004. LNCS, vol. 3340, pp. 76–88. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    ter Beek, M.H., Csuhaj–Varjú, E., Holzer, M., Vaszil, G.: On Competence in CD Grammar Systems with Parallel Rewriting. International Journal of Foundations of Computer Science 18, 1425–1439 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Csuhaj–Varjú, E., Dassow, J., Holzer, M.: CD Grammar Systems with Competence Based Entry Conditions in their Cooperation Protocols. International Journal of Computer Mathematics 83, 159–169 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    von Solms, S.H.: Some Notes on ET0L-languages. International Journal of Computer Mathematics 5, 285–296 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Bordihn, H., Holzer, M.: Grammar Systems with Negated Conditions in their Cooperation Protocols. Journal of Universal Computer Science 6, 1165–1184 (2000)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Fernau, H., Wätjen, D.: Remarks on Regulated Limited ET0L Systems and Regulated Context-Free Grammars. Theoretical Computer Science 194, 35–55 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. EATCS Monographs in Theoretical Computer Science, vol. 18. Springer, Berlin (1989)CrossRefzbMATHGoogle Scholar
  13. 13.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. 1-3. Springer, Berlin (1997)zbMATHGoogle Scholar
  14. 14.
    Bordihn, H., Holzer, M.: Personal communicationGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Maurice H. ter Beek
    • 1
  • Erzsébet Csuhaj-Varjú
    • 2
  • Markus Holzer
    • 3
  • György Vaszil
    • 2
  1. 1.Istituto di Scienza e Tecnologie dell’Informazione ‘A. Faedo’Consiglio Nazionale delle RicerchePisaItaly
  2. 2.Computer and Automation Research InstituteHungarian Academy of SciencesBudapestHungary
  3. 3.Institut für InformatikUniversität GiessenGiessenGermany

Personalised recommendations