Multiset and K-Subset Transforming Systems

  • Taishin Yasunobu Nishida
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2235)

Abstract

We introduce K-subset transforming systems as a generalization of multiset transformation. A K-subset, which is a generalization of a multiset where “multiplicities” take values in a semiring, is considered by S. Eilenberg. We construct an example of K-subset transforming system which models a chaotic discrete dynamical system. We show that for every basic reaction of multiset transformation we can construct a K-subset transforming system which expresses the multiset transformation. We also show that for every phrase structure grammar there is a K-subset transforming system such that the system simulates derivations of the grammar.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. Banâtre, A. Coutant, and D. Le Metayer, A parallel machine for multiset transformation and its programming style, Future Generations Computer Systems, 4 (1988), 133–144.CrossRefGoogle Scholar
  2. 2.
    J. Banâtre and D. Le Métayer, Programming by multiset transformation, Communications of the ACM, 36 (1993), 98–111.CrossRefGoogle Scholar
  3. 3.
    J. Dassow and G. Păun, On the power of membrane computing, Journal of Universal Computer Science, 5 (1999), 33–49.Google Scholar
  4. 4.
    W. D. Blizard, The development of multiset theory, Modern Logic, 1 (1991), 319–3522.MATHMathSciNetGoogle Scholar
  5. 5.
    S. Eilenberg, Automata, Languages, and Machines Volume A, Academic Press, New York, 1974.MATHGoogle Scholar
  6. 6.
    C. Hankin, D. Le Métayer, and D. Sands, Refining multiset transformers, Theoretical Computer Science, 192 (1998), 233–258.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    G. T. Herman and G. Rozenberg, Developmental Systems and Languages, North-Holland, Amsterdam, 1975.Google Scholar
  8. 8.
    M. Martelli, Discrete Dynamical Systems and Chaos, Longman Scientific & Technical, Harlow, 1992.MATHGoogle Scholar
  9. 9.
    G. Păun, Computing with membranes, Journal of Computer and System Sciences, 61 (2000), 108–143, (and Turku Centre for Computer Science-TUCS Report No 208, 1998 (http://www.tucs..)).CrossRefMathSciNetMATHGoogle Scholar
  10. 10.
    G. Păun, Computing with membranes. An introduction, Bulletin of the EATCS 67 (1999) 139–152.MATHGoogle Scholar
  11. 11.
    G. Păun, P systems: an early survey, The Third International Colloquium on Words, Languages and Combinatorics March 2000, Kyoto (Proceedings will be published by World Scientific, Singapore).Google Scholar
  12. 12.
    G. Păun, G. Rozenberg, and A. Salomaa, DNA Computing, Springer-Verlag, Berlin, 1998.MATHGoogle Scholar
  13. 13.
    A. Salomaa, Formal Languages, Academic Press, New York, 1973.MATHGoogle Scholar
  14. 14.
    P. W. Shor, Algorithm for quantum computation: discrete log and factoring, in: Proceedings of the 35th Annual IEEE Symposium on Foundations of Computer Science, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Taishin Yasunobu Nishida
    • 1
  1. 1.Faculty of EngineeringToyama Prefectural UniversityToyamaJapan

Personalised recommendations