Advertisement

Grammar systems as language analyzers and recursively enumerable languages

  • Henning Bordihn
  • Júrgen Dassow
  • Gyorgy Vaszil
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1684)

Abstract

We consider parallel communicating grammar systems which consist of several grammars and perform derivation steps, where each of the grammars works in a parallel and synchronized manner on its own sentential form, and communication steps, where a transfer of sentential forms is done. We discuss accepting and analyzing versions of such grammar systems with context-free productions and present characterizations of the family of recursively enumerable languages by them.

In accepting parallel communicating grammar systems rules of the form α → A with a word α and a nonterminal A are applied as in the generating case, and the language consists of all terminal words which can derive the axiom. We prove that all types of these accepting grammar systems describe the family of recursively enumerable languages, even if Λ-rules are forbidden.

Moreover, we study analyzing parallel communicating grammar systems, the derivations of which perform the generating counterparts backwards. This requires a modication of the generating derivation concept to strong-returning parallel communicating grammar systems which also generate the family of recursively enumerable languages.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    H. Bordihn and H. Fernau, Accepting grammars and systems. Technical Report 9/94, Universität Karlsruhe, Fakultät für Informatik, 1994.Google Scholar
  2. [2]
    H. Bordihn and H. Fernau, Accepting grammars with regulation. Intern. J. Comp. Math. 53 (1994) 1–18.zbMATHCrossRefGoogle Scholar
  3. [3]
    H. Bordihn and H. Fernau, Accepting grammars and systems via context condition grammars. Journal of Automata, Languages and Combinatorics 1 (1996) 97–112.zbMATHMathSciNetGoogle Scholar
  4. [4]
    E. Csuhaj-Varjú, J. Dassow, J. Kelemen and Gh. Păun, Grammar Systems: A Grammatical Approach to Distribution and Cooperation. Volume 5 of Topics in Computer Mathematics. Gordon and Breach, 1994.Google Scholar
  5. [5]
    E. Csuhaj-Varjú and Gy. Vaszil, On context-free parallel communicating grammar systems: synchronization, communication, and normal forms. Accepted for publication in Theoretical Computer Science.Google Scholar
  6. [6]
    E. Csuhaj-Varjú and Gy. Vaszil, On the computational completeness of context-free parallel communicating grammar systems. Theor. Comp. Sci. 215 1-2 (1999), 349–358.zbMATHCrossRefGoogle Scholar
  7. [7]
    J. Dassow, Gh. Păun and G. Rozenberg, Grammar systems. In: A. Salomaa and G. Rozenberg (ed.), Handbook of Formal Languages, Vol. 2, Chapter 4, Springer-Verlag, Berlin-Heidelberg, 1996, 155–213.Google Scholar
  8. [8]
    H. Fernau and H. Bordihn, Remarks on accepting parallel systems. Intern. J. Comp. Math. 56 (1995) 51–67.zbMATHCrossRefGoogle Scholar
  9. [9]
    H. Fernau, M. Holzer and H. Bordihn, Accepting multi-agent systems: the case of cooperating distributed grammar systems. Computers and Articial Intelligence 15 (1996) 123–139.zbMATHMathSciNetGoogle Scholar
  10. [10]
    J. Hromkovič, On the communication complexity of distributive language generation. In: J. Dassow, G. Rozenberg and A. Salomaa (ed.), Developments in Language Theory II, World Scientic Publ. Co. Pte. Ltd., 1995, 237–246.Google Scholar
  11. [11]
    N. Mandache, On the computational power of context-free PCGSs. Submitted.Google Scholar
  12. [12]
    A. Mateescu and A. Salomaa, Aspects of classical language theory. In: A. Salomaa and G. Rozenberg (ed.), Handbook of Formal Languages, Vol. 1, Chapter 4, Springer-Verlag, Berlin-Heidelberg, 1996, 175–251.Google Scholar
  13. [13]
    V. Mihalache, Accepting cooperating distributed grammar systems with terminal derivation. EATCS Bulletin 61 (1997) 80–84.zbMATHGoogle Scholar
  14. [14]
    Gh. Păun, On the synchronization in parallel communicating grammar systems. Acta Informatica 30 (1993) 351–367.CrossRefMathSciNetzbMATHGoogle Scholar
  15. [15]
    Gh. Păun and L. Santean, Parallel communicating grammar systems: the regular case. Ann. Univ. Buc. Ser. Mat.-Inform. 37 (1989) 55–63.Google Scholar
  16. [16]
    A. Salomaa, Formal Languages. Academic Press, 1973.Google Scholar
  17. [17]
    F. L. Ţiplea, C. Ene, C. M. Ionescu and O. Procopiuc. Some decision problems for parallel communicating grammar systems. Theor. Comp. Sci. 134 (1994) 365–385.CrossRefzbMATHGoogle Scholar
  18. [18]
    Gy. Vaszil, On simulating non-returning PC grammar systems with returning systems. Theor. Comp. Sci. 209 (1998), 319–329.zbMATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    Gy. Vaszil, On parallel communicating Lindenmayer systems, In: Gh. Păun and A. Salomaa (ed.), Grammatical Models of Multi-Agent Systems, Gordon and Breach, 1999, 99–112.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Henning Bordihn
    • 1
  • Júrgen Dassow
    • 1
  • Gyorgy Vaszil
    • 2
  1. 1.Fakultä at für InformatikOtto-von-Guericke-Universitä at MagdeburgMagdeburgGermany
  2. 2.Hungarian Academy of SciencesComputer and Automation Research InstituteBudapestHungary

Personalised recommendations