Topological Collections, Transformations and Their Application to the Modeling and the Simulation of Dynamical Systems

  • Jean-Louis Giavitto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2706)


I take the opportunity given by this invited talk to promote two ideas: (1) a topological point of view can fertilize the notion of rewriting and (2) this topological approach of rewriting is at the core of the modeling and the simulation of an emerging class of dynamical systems (DS): the DS that exhibit a dynamical structure (or (DS)2 in the rest of this paper).


Cellular Automaton Cellular Automaton Cayley Graph Delaunay Triangulation Collection Type 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. ACD02.
    J.J. Arulanandham, C.S. Calude, and M.J. Dinneen. Bead-sort: A natural sorting algorithm. Bulletin of the European Association for Theoretical Computer Science, 76:153–162, February 2002. Technical Contributions.MATHMathSciNetGoogle Scholar
  2. BB90.
    G. Berry and G. Boudol. The chemical abstract machine. In Conf. Record 17th ACM Symp. on Principles of Programmming Languages, POPL’90, San Francisco, CA, USA, 17–19 Jan. 1990, pages 81–94. ACM Press, New York, 1990.Google Scholar
  3. BCM87.
    J. P. Banâtre, A. Coutant, and Daniel Le Métayer. Parallel machines for multiset transformation and their programming style. Technical Report RR-0759, Inria, 1987.Google Scholar
  4. BLL97.
    F. Bergeron, G. Labelle, and P. Leroux. Combinatorial species and tree-like structures, volume 67 of Encyclopedia of mathematics and its applications. Cambridge University Press, 1997. isbn 0-521-57323-8.Google Scholar
  5. BM86.
    J. P. Banâtre and Daniel Le Métayer. A new computational model and its discipline of programming. Technical Report RR-0566, Inria, 1986.Google Scholar
  6. BNTW95.
    Peter Buneman, Shamim Naqvi, Val Tannen, and Limsoon Wong. Principles of programming with complex objects and collection types. Theoretical Computer Science, 149(1):3–48, 18 September 1995.MATHCrossRefMathSciNetGoogle Scholar
  7. Ede58.
    M. Eden. In H. P. Yockey, editor, Symposium on Information Theory in Biology, page 359, New York, 1958. Pergamon Press.Google Scholar
  8. EKL+02a._S. Eker, M. Knapp, K. Laderoute, P. Lincoln, J. Meseguer, and J. Sonmez. Pathway logic: Symbolic analysis of biological signaling. In Proceedings of the Pacific Symposium on Biocomputing, pages 400–412, January 2002.Google Scholar
  9. EKL+02b._Steven Eker, Merrill Knapp, Keith Laderoute, Patrick Lincoln, and Carolyn Talcott. Pathway logic: Executable models of biological networks. In Fourth International Workshop on Rewriting Logic and Its Applications (WRLA’2002), volume 71 of Electronic Notes in Theoretical Computer Science. Elsevier, 2002.Google Scholar
  10. FM97.
    P. Fradet and D. Le Métayer. Shape types. In Proc. of Principles of Programming Languages, Paris, France, Jan. 1997. ACM Press.Google Scholar
  11. FMP00.
    Michael Fisher, Grant Malcolm, and Raymond Paton. Spatio-logical processes in intracellular signaling. BioSystems, 55:83–92, 2000.CrossRefGoogle Scholar
  12. FS96.
    Leonidas Fegaras and Tim Sheard. Revisiting catamorphisms over datatypes with embedded functions (or, Programs from outer space). In Conference Record of POPL’ 96: The 23rd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 284–294, St. Petersburg Beach, Florida, 21–24 January 1996.Google Scholar
  13. GG95.
    D. Gautier and C. Germain. A static approach for compiling communications in parallel scientific programs. Scientific Programming, 4:291–305, 1995.Google Scholar
  14. GGMP02.
    J.-L. Giavitto, C. Godin, O. Michel, and P. Prusinkiewicz. Modelling and Simulation of biological processes in the context of genomics, chapter “Computational Models for Integrative and Developmental Biology”. Hermes, July 2002.Google Scholar
  15. Gia00.
    J.-L. Giavitto. A framework for the recursive definition of data structures. In ACM-Sigplan 2nd International Conference on Principles and Practice of Declarative Programming (PPDP’00), pages 45–55, Montréal, September 2000. ACM-press.Google Scholar
  16. GJ92.
    E. Goubault and T. P. Jensen. Homology of higher-dimensional automata. In Proc. of CONCUR’92, Stonybrook, August 1992. Springer-Verlag.Google Scholar
  17. GM01a.
    J.-L. Giavitto and O. Michel. Declarative definition of group indexed data structures and approximation of their domains. In Proceedings of the 3nd International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming (PPDP-01). ACM Press, September 2001.Google Scholar
  18. GM01b.
    J.-L. Giavitto and O. Michel. MGS: a programming language for the transformations of topological collections. Technical Report 61-2001, LaMI — Université d’évry Val d’Essonne, May 2001.Google Scholar
  19. GM01c.
    Jean-Louis Giavitto and Olivier Michel. Mgs: a rule-based programming language for complex objects and collections. In Mark van den Brand and Rakesh Verma, editors, Electronic Notes in Theoretical Computer Science, volume 59. Elsevier Science Publishers, 2001.Google Scholar
  20. GM02a.
    J.-L. Giavitto and O. Michel. Data structure as topological spaces. In Proceedings of the 3nd International Conference on Unconventional Models of Computation UMC02, volume 2509, pages 137–150, Himeji, Japan, October 2002. Lecture Notes in Computer Science.CrossRefGoogle Scholar
  21. GM02b.
    J.-L. Giavitto and O. Michel. The topological structures of membrane computing. Fundamenta Informaticae, 49:107–129, 2002.MathSciNetGoogle Scholar
  22. GMC02.
    J.-L. Giavitto, O. Michel, and J. Cohen. Pattern-matching and rewriting rules for group indexed data structures. Technical Report 76-2002, LaMI — Université d’évry Val d’Essonne, June 2002.Google Scholar
  23. GMS95.
    J.-L. Giavitto, O. Michel, and J.-P. Sansonnet. Group based fields. In I. Takayasu, R. H. Jr. Halstead, and C. Queinnec, editors, Parallel Symbolic Languages and Systems (International Workshop PSLS’95), volume 1068 of LNCS, pages 209–215, Beaune (France), 2–4 October 1995. Springer-Verlag.CrossRefGoogle Scholar
  24. Hen94.
    M. Henle. A combinatorial introduction to topology. Dover publications, New-York, 1994.MATHGoogle Scholar
  25. Jam93.
    Max Jammer. Concepts of space — the history of theories of space in physics. Dover, 1993. third enlarged edition (first edition 1954).Google Scholar
  26. Jay95.
    C. Barry Jay. A semantics of shape. Science of Computer Programming, 25(2–3):251–283, 1995.MATHMathSciNetGoogle Scholar
  27. Lie91.
    P. Lienhardt. Topological models for boundary representation: a comparison with n-dimensional generalized maps. Computer-Aided Design, 23(1):59–82, 1991.MATHCrossRefGoogle Scholar
  28. Lin68.
    A. Lindenmayer. Mathematical models for cellular interaction in development, Parts I and II. Journal of Theoretical Biology, 18:280–315, 1968.CrossRefGoogle Scholar
  29. Lis93.
    B. Lisper. On the relation between functional and data-parallel programming languages. In Proc. of the 6th. Int. Conf. on Functional Languages and Computer Architectures. ACM, ACM Press, June 1993.Google Scholar
  30. Man01.
    Vincenzo Manca. Logical string rewriting. Theoretical Computer Science, 264:25–51, 2001.MATHCrossRefMathSciNetGoogle Scholar
  31. MFP91.
    E. Meijer, M. Fokkinga, and R. Paterson. Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire. In 5th ACM Conference on Functional Programming Languages and Computer Architecture, volume 523 of Lecture Notes in Computer Science, pages 124–144, Cambridge, MA, August 26–30, 1991. Springer, Berlin.Google Scholar
  32. NO94.
    Susumu Nishimura and Atsushi Ohori. A calculus for exploiting data parallelism on recursively defined data (Preliminary Report). In International Workshop TPPP’ 94 Proceedings (LNCS 907), pages 413–432. Springer-Verlag, November 94.Google Scholar
  33. Pau98.
    G. Paun. Computing with membranes. Technical Report TUCS-TR-208, TUCS — Turku Centre for Computer Science, November 11 1998.Google Scholar
  34. Pau01.
    G. Paun. From cells to computers: Computing with membranes (p systems). Biosystems, 59(3):139–158, March 2001.CrossRefGoogle Scholar
  35. PH92.
    P. Prusinkiewicz and J. Hanan. L systems: from formalism to programming languages. In G. Ronzenberg and A. Salomaa, editors, Lindenmayer Systems, Impacts on Theoretical Computer Science, Computer Graphics and Developmental Biology, pages 193–211. Springer Verlag, February 1992.Google Scholar
  36. PLH+90.
    P. Prusinkiewicz, A. Lindenmayer, J. S. Hanan, et al. The Algorithmic Beauty of Plants. Springer-Verlag, 1990.Google Scholar
  37. Rók94.
    Zsuzsanna Róka. One-way cellular automata on Cayley graphs. Theoretical Computer Science, 132(1–2):259–290, 26 September 1994.MATHCrossRefMathSciNetGoogle Scholar
  38. Wol02.
    Stephen Wolfram. A new kind of science. Wolfram Media, 2002.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jean-Louis Giavitto
    • 1
  1. 1.CNRS — LaMI, umr 8042Université d’évry — GENOPOLEÉvryFrance

Personalised recommendations