Multiset Automata

  • Erzsébet Csuhaj-Varjú
  • Carlos Martín-Vide
  • Victor Mitrana
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2235)


We propose a characterization of a Chomsky-like hierarchy of multiset grammars in terms of multiset automata. We also present the deterministic variants of all the automata investigated and prove that, unlike the string case, most of them are strictly less powerful than the nondeterministic variants. Some open problems and further directions of research are briefly discussed.




Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J.P. Banătre, A. Coutant, D. Le Metayer, A parallel machine for multiset transformation and its programming style, Future Generation Computer Systems, 4 (1988), 133–144.CrossRefGoogle Scholar
  2. 2.
    J. P. Banătre, D. Le Metayer, Gamma and chemical reaction model: ten years after, Coordination Programming: Mechanisms, Models and Semantics (C. Hankin, ed.), Imperial College Press, 1996.Google Scholar
  3. 3.
    G. Berry, G. Boudol, The chemical abstract machine, Theoretical Computer Sci., 96 (1992), 217–248.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    A.B. Cremers, Normal forms for context-sensitive grammars, Acta Informatica, 3 (1973), 59–73.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    S. Crespi-Reghizzi, D. Mandrioli, Commutative grammars, Calcolo, 13, 2, (1976), 173–189.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    J. Gonczarowski, M.K. Warmuth, Scattered versus context-sensitive rewriting, Acta Informatica, 27 (1989), 81–95.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    S. Greibach, J. Hopcroft, Scattered context grammars, J. Comput. Syst. Sci., 3 (1969), 233–247.MATHMathSciNetGoogle Scholar
  8. 8.
    R. Helm, K. Marriott, M. Odersky, Building visual language parsers, Proc. ACM Conf. Human Factors in Computing, 1991.Google Scholar
  9. 9.
    M. Kudlek, C. Martin-Vide, G. Păun, Toward FMT (Formal Macroset Theory), Pre-Proceedings of the Workshop on Multiset Processing (WMP’2000) (C.S. Calude, M.J. Dinneen, G. Păun, eds.), CDMTCS-140, 2000, 149–158.Google Scholar
  10. 10.
    M. Latteux, Cones rationnels commutatifs, J. of Computer and System Sciences, 18 (1979), 307–333.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    K. Marriott, Constraint multiset grammars, Proc. IEEE Symposium on Visual Languages (A. L. Ambler, T. Kimura, eds.), IEEE Comp. Soc. Press, 1994, 118–125.Google Scholar
  12. 12.
    G. Păun, G. Rozenberg, A. Salomaa, DNA Computing. New Computing Paradigms, Springer-Verlag, Berlin, 1998.MATHGoogle Scholar
  13. 13.
    G. Păun, Computing with membranes J. of Computer and System Sciences, 61, 1 (2000), 108–143CrossRefMATHGoogle Scholar
  14. 14.
    G. Păun, Computing with membranes (P systems): Twenty six research topics, CDMTCS ReportNo. 119, Auckland University, 2000.Google Scholar
  15. 15.
    G. Rozenberg, A. Salomaa, eds., Handbook of Formal Languages, 3 volumes, Springer-Verlag, Berlin, 1997.MATHGoogle Scholar
  16. 16.
    Y. Suzuki, H. Tanaka, Symbolic chemical system based on abstract rewriting system and its behavior pattern, Artificial Life Robotics, 1 (1997), 211–219.CrossRefGoogle Scholar
  17. 17.
    Y. Suzuki, H. Tanaka, Chemical evolution among artificial proto-cells, Proc. of Artificial Life VIII Conf., MIT Press, 2000.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Erzsébet Csuhaj-Varjú
    • 1
  • Carlos Martín-Vide
    • 2
  • Victor Mitrana
    • 3
  1. 1.Computer and Automation Research InstituteHungarian Academy of SciencesBudapestHungary
  2. 2.Research Group on Mathematical LinguisticsRovira i Virgili UniversityTarragonaSpain
  3. 3.University of Bucharest, Faculty of MathematicsBucharestRomania

Personalised recommendations