Artificial Life Applications of a Class of P Systems: Abstract Rewriting Systems on Multisets

  • Yasuhiro Suzuki
  • Yoshi Fujiwara
  • Junji Takabayashi
  • Hiroshi Tanaka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2235)


Artificial chemical system are well studied in Artificial Life and Complexity. Here we overview results about such a class of artificial chemical systems: Abstract Rewriting Systems on Multisets (ARMS), which are particular types of P Systems and exhibit complex behaviors such as non-linear oscillations. In short, an ARMS consists of a membrane which contains “chemical compounds” (denoted by symbols); these compounds evolve through chemical reactions in a cell-like device. To such systems we apply a genetic method and, by a simulation on computer, we find several results of Artificial Life interest.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    W. Banzaf, Self-replicating sequences of numbers — foundation I and II: General and strings of length n = 4, Biological Cybernetics, (69), 269–281, 1993.CrossRefGoogle Scholar
  2. 2.
    C.L. Barrett and C.M. Reidys, Elements of a theory of computer simulation I: Sequential CA over random graphs, Appl. Math. and Comp., (to appear).Google Scholar
  3. 3.
    C.L. Barrett, H.S. Mortiveit H.S. and C.M. Reidys, Elements of a theory of computer simulation II: Sequential dynamical systems, Appl. Math. and Comp., (to appear).Google Scholar
  4. 4.
    R. Begley and D. Farmer, Spontaneous emergence of a metabolism, Artificial Life II, pp141–158, Addison-Wesley, 1991Google Scholar
  5. 5.
    G. Berry and G. Boudol. 1992. The chemical abstract machine. Theoretical Computer Science 96: 217–248.Google Scholar
  6. 6.
    H. Bersini, Reaction mechanisms in the oo chemistry, Artificial Life VII, pp39–48, MIT press, 2000Google Scholar
  7. 7.
    B. Bollobas, Random Graphs, Academic Press, 1985Google Scholar
  8. 8.
    C. Calude, Gh. Păun, Computing with Cells and Atoms, Taylor and Francis, London, 2000 (Chapter 3: “Computing with Membranes”).Google Scholar
  9. 9.
    J. Dassow, Gh. Păun, Regulated Rewriting in Formal Language Theory, Springer-Verlag, Berlin, 1989.Google Scholar
  10. 10.
    J. Dassow, Gh. Păun, On the power of membrane computing, J. of Universal Computer Sci., 5, 2 (1999), 33–49 ( Scholar
  11. 11.
    J. Takabayashi and Dicke, M. Plant-carnivore mutualism through herbivoreinduced carnivore attractants, Trends in Plant Science 1: 109–113, 1996.CrossRefGoogle Scholar
  12. 12.
    M. Dicke, J. Takabayashi, C. Schütte, O.R. Krips, Behavioral ecology of plantcarnivore interactions: variation in response of phytoseiid mites to herbivoreinduced plant volatiles. Experimental and Applied Acarology 22: 595–601, 1997.Google Scholar
  13. 13.
    P. Dittrich, J. Ziegler and W. Banzaf, Artificial Chemistries — A Review,
  14. 14.
    P. Dittrichi and Banzaf W., Self-evolution in constructive binary string system, Artificial Life 4(2), pp 203–220, MIT press, 1998.CrossRefGoogle Scholar
  15. 15.
    M. Eigen and P. Schuster, The Hypercycle, Springer-Verlag, 1979.Google Scholar
  16. 16.
    D.S. Fenizio, A less abstract artificial chemistry, Artificial Life VII, pp 49–53, MIT press, 2000Google Scholar
  17. 17.
    W. Fontana, Algorithmic Chemistry, Artificial Life II, 160–209, Addison Wesley, 1994.Google Scholar
  18. 18.
    W. Fontana, L. W. Buss, The arrival of the fittest: Toward a theory of biological organization, Bulletin of Mathematical Biology, 56 (1994), 1–64.MATHGoogle Scholar
  19. 19.
    D. Frijtyers and A. Lindenmayer, L systems, Lecture Notes In Computer Science, vol. 15, Springer Verlag, 1994.Google Scholar
  20. 20.
    J. H. Gallier, Logic for Computer Science, p 89, John Wiley & Sons, 1987.Google Scholar
  21. 21.
    M. R. Garey, D. J. Johnson, Computers and Intractability. A Guide to the Theory of NP-Completeness, W. H. Freeman and Comp., San Francisco, 1979.Google Scholar
  22. 22.
    M. J. O’Donnell, Computing in system described by equations, Lecture Note in Computer Science, Vol.58, Springer Verlag, 1977.Google Scholar
  23. 23.
    C. Epstain, and R. Butow, Microarray technology-enhanced versatility, persistent challenge, Curr. Opin. Biotech, 11, 36–41, 2000CrossRefGoogle Scholar
  24. 24.
    P. Erdös and A. Reny, On random graphs, Publicationes Mathematicae, 6, 290–297, 1959.MATHGoogle Scholar
  25. 25.
    W. Feller, An Introduction to Probability Theory and Its Applications, I, 1957.Google Scholar
  26. 26.
    R.J. Field and M. Burger. 1985. Oscillations and Traveling Waves in Chemical Systems. John Wiley and Sons.Google Scholar
  27. 27.
    C. W. Gardiner, Handbook of Stochastic Methods, 2nd edition, (Springer-Verlag, 1985).Google Scholar
  28. 28.
    J. Guare, Six Degrees of Separation, A Play, Vintage, 1990.Google Scholar
  29. 29.
    J. E. Hopcroft and J. D. Ullman, Introduction to Automata theory, Languages and Computation, Addison-Wesley, 1979.Google Scholar
  30. 30.
    G. Huet and D. S. Lankford, On the Uniform halting problem for Term Rewriting Systems, Rapport 359, IN-RIA, 1978.Google Scholar
  31. 31.
    N. G. van Kampen, Stochastic Processes in Physics and Chemistry, (North-Holland, 1981).Google Scholar
  32. 32.
    S. A. Kauffman, The Origins of Order, Oxford University Press, 1993.Google Scholar
  33. 33.
    J. W. Klop, Term Rewriting System, in S. Abramsky, Don M. Gabby and T. S. E. Maibaum, edit, Handbook of Logic in Computer Science, 3–62, Clarendon Press, 1992.Google Scholar
  34. 34.
    D. E. Knuth and P. B. Bendix, Simple word problems in universal algebras, North-Holland, 1985.Google Scholar
  35. 35.
    S. N. Krishna, R. Rama, A variant of P systems with active membranes: Solving NP-complete problems, Romanian J. of Information Science and Technology, 2, 4 (1999), 357–367.Google Scholar
  36. 36.
    C. G. Langton, Life at the edge of chaos. In Artificial Life II, edited by C. G. Langton, C. Taylor, J. D. Farmer, and S. Rasmussen. Redwood City, CA: Addison Wesley, 1991.Google Scholar
  37. 37.
    P.L. Luisi, The chemical implementation of autopoiesis, Self-production of Supramolecular structures, pp 179–197, Kluwer Academic publ. 1994Google Scholar
  38. 38.
    H. R. Maturana and F. J. Varela, Autopoiesis and Cognition, D. Reidel Publishing Company, 1980.Google Scholar
  39. 39.
    B. McMullin and F. Varela, Rediscovering Computational Autopoiesis, ECAL’97. 1997.Google Scholar
  40. 40.
    K. Mirazo, A. Moreno, F. Moran, et. al., Designing a Simulation Model of a Self-Maintaining Cellular System ECAL’97. 1997.Google Scholar
  41. 41.
    R. B. Nachbar, Molecular evolution: Automed manipulation of hierarchical chemical topology and its application to average molecular structures, Genetic Programming and Evolvable Machines, 1(1/2):54–94, 2000CrossRefGoogle Scholar
  42. 42.
    M.E.J. Newman, Small Worlds, Santa Fe Institute Working Paper, 1999.Google Scholar
  43. 43.
    G. Nicolis and I. Prigogine. 1989. Exploring Complexity, An Introduction. San Francisco: Freeman and Company.Google Scholar
  44. 44.
    T. Maeda, J. Takabayashi, J., Yano, A. Takafuji, Factors affecting the resident time of the predatory mite Phytoseiulus persimilis (Acari: Phytoseiidae) in a prey patch, Applied Entomology and Zoology 33: 573–576, 1998Google Scholar
  45. 45.
    AI. Oparin, KB. Serebrovskaya, SN. Pantskhava and NV. Vesil’eva. Enzymatic synthesis of polyadenylic acid in coacervate drops. Biokhimiya 28, 4, 671–643, 1963Google Scholar
  46. 46.
    Gh. Păun, Y. Suzuki, H. Tanaka, P Systems with energy accounting, Intern. J. Computer Math., 79, 3/4 (in print)Google Scholar
  47. 47.
    Gh. Păun, P systems with active membranes: Attacking NP complete problems, J. Automata, Languages and Combinatorics, 6, 1 (2001), 75–93.MATHGoogle Scholar
  48. 48.
    Gh. Păun, Y. Sakakibara, T. Yokomori, P systems on graphs of restricted forms, submitted, 1999.Google Scholar
  49. 49.
    Gh. Păun, Computing with membranes, Journal of Computer and System Sciences, 61, 1 (2000), 108–143, and Turku Center for Computer Science-TUCS Report No 208, 1998 (www.tucs..).CrossRefMathSciNetMATHGoogle Scholar
  50. 50.
    G. Rozenberg and A. Salomaa, The Mathematical Theory of L Systems, Academic Press, New York, 1980.MATHGoogle Scholar
  51. 51.
    Sabelis, M.W. amd De jong, M.C.M. shyould all plants recruit bodygurads? Conditions for a polymorphic ESS of synomone production in plants. Oikos, 53: 247–252, 1988.CrossRefGoogle Scholar
  52. 52.
    R. Smogyl,, Cluster Analysis and data visualization of largescale gene expression data, Pacific Symposium on Biocomputing, 3, 42–53, 1999.Google Scholar
  53. 53.
    Y. Suzuki and H. Tanaka, Symbolic chemical system based on abstract rewriting system and its behavior pattern, Journal of Artificial Life and Robotics, 1 (1997), 211–219.CrossRefGoogle Scholar
  54. 54.
    Y. Suzuki and H. Tanaka, Order parameter for a symbolic chemical system, Artificial Life VI, MIT Press, 1998, 130–139.Google Scholar
  55. 55.
    Y. Suzuki and H. Tanaka, Artificial proto-cell based on symbolic chemical systems, submitted, 1999.Google Scholar
  56. 56.
    Y. Suzuki, S. Tsumoto, H. Tanaka, Analysis of cycles in symbolic chemical systems based on abstract rewriting systems on multisets, Artificial Life V, MIT Press, 1996, 522–528.Google Scholar
  57. 57.
    Y. Suzuki and H. Tanaka. 1997. Chemical oscillation on symbolic chemical systems and its behavioral pattern. In Proceedings of the International Conference on Complex Systems, Nashua, NH, 21-26 Sept 1997.Google Scholar
  58. 58.
    Y. Suzuki and H. Tanaka, On a LISP implementation of a class of P systems, Romanian J. of Information Science and Technology, 3, 2 (2000).Google Scholar
  59. 59.
    H. Tanaka, F. Ren, S. Ogishima, Evolutionary Analysis of Virus Based on Inhomogeneous Markov Model, ISMB’99, p 148, 1999.Google Scholar
  60. 61.
    P. Walde, A. Goto, A. Monnard,, Oparin’s reactions revised: enzymatic synthesis of poly i micelles and self-reproducing vesicles, J. Am. Chem. Soc., 116, 7541–7574, 1994CrossRefGoogle Scholar
  61. 62.
    D. J. Watts, Small Worlds, Princeton Univ. Press, 1999Google Scholar
  62. 63.
    J. D. Watson, N. H. Hopkins at el, Molecular biology of the gene, The Benjamin/Cummings publishing Company, Inc, 1992.Google Scholar
  63. 64.
    S. Wolfram, Cellular Automata and Complexity, 1994.Google Scholar
  64. 65.
    S. Wolfram, 1984a. Computation theory of cellular automaton. Commun. Math. Phys. 96: 15–57.Google Scholar
  65. 66.
    S. Wolfram, 1984b Universality and complexity in cellular automata. Physica D 10: 1–35.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Yasuhiro Suzuki
    • 1
  • Yoshi Fujiwara
    • 2
  • Junji Takabayashi
    • 3
  • Hiroshi Tanaka
    • 1
  1. 1.Bio-Informatics, Medical Research InstituteTokyo Medical and Dental UniversityTokyoJapan
  2. 2.Keihanna CenterCommunications Research LaboratoryKyotoJapan
  3. 3.Center for Ecological ResearchKyoto UniversityKamitanakami, OtsuJapan

Personalised recommendations