Skip to main content
SpringerLink
Log in

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

  • Conference paper
  • First Online:
Rewriting Techniques and Applications (RTA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2706))

Included in the following conference series:

Abstract

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).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. 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.

    MATH  MathSciNet  Google Scholar 

  2. 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. 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. 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. 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. 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.

    Article  MATH  MathSciNet  Google Scholar 

  7. 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. P. Fradet and D. Le Métayer. Shape types. In Proc. of Principles of Programming Languages, Paris, France, Jan. 1997. ACM Press.

    Google Scholar 

  11. Michael Fisher, Grant Malcolm, and Raymond Paton. Spatio-logical processes in intracellular signaling. BioSystems, 55:83–92, 2000.

    Article  Google Scholar 

  12. 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. D. Gautier and C. Germain. A static approach for compiling communications in parallel scientific programs. Scientific Programming, 4:291–305, 1995.

    Google Scholar 

  14. 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. 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. E. Goubault and T. P. Jensen. Homology of higher-dimensional automata. In Proc. of CONCUR’92, Stonybrook, August 1992. Springer-Verlag.

    Google Scholar 

  17. 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. 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. 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. 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.

    Chapter  Google Scholar 

  21. J.-L. Giavitto and O. Michel. The topological structures of membrane computing. Fundamenta Informaticae, 49:107–129, 2002.

    MathSciNet  Google Scholar 

  22. 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. 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.

    Chapter  Google Scholar 

  24. M. Henle. A combinatorial introduction to topology. Dover publications, New-York, 1994.

    MATH  Google Scholar 

  25. Max Jammer. Concepts of space — the history of theories of space in physics. Dover, 1993. third enlarged edition (first edition 1954).

    Google Scholar 

  26. C. Barry Jay. A semantics of shape. Science of Computer Programming, 25(2–3):251–283, 1995.

    MATH  MathSciNet  Google Scholar 

  27. P. Lienhardt. Topological models for boundary representation: a comparison with n-dimensional generalized maps. Computer-Aided Design, 23(1):59–82, 1991.

    Article  MATH  Google Scholar 

  28. A. Lindenmayer. Mathematical models for cellular interaction in development, Parts I and II. Journal of Theoretical Biology, 18:280–315, 1968.

    Article  Google Scholar 

  29. 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. Vincenzo Manca. Logical string rewriting. Theoretical Computer Science, 264:25–51, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  31. 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. 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. G. Paun. Computing with membranes. Technical Report TUCS-TR-208, TUCS — Turku Centre for Computer Science, November 11 1998.

    Google Scholar 

  34. G. Paun. From cells to computers: Computing with membranes (p systems). Biosystems, 59(3):139–158, March 2001.

    Article  Google Scholar 

  35. 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. P. Prusinkiewicz, A. Lindenmayer, J. S. Hanan, et al. The Algorithmic Beauty of Plants. Springer-Verlag, 1990.

    Google Scholar 

  37. Zsuzsanna Róka. One-way cellular automata on Cayley graphs. Theoretical Computer Science, 132(1–2):259–290, 26 September 1994.

    Article  MATH  MathSciNet  Google Scholar 

  38. Stephen Wolfram. A new kind of science. Wolfram Media, 2002.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CNRS — LaMI, umr 8042, Université d’évry — GENOPOLE, Tour Evry-2, 523 Place des Terrasses de l’Agora, 91000, Évry, France

    Jean-Louis Giavitto

Authors
  1. Jean-Louis Giavitto
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dpt. Lenguajes y Sistemas Informáticos (LSI), Technical University of Catalonia (UPC), Jordi Girona 1, 08034, Barcelona, Spain

    Robert Nieuwenhuis

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Giavitto, JL. (2003). Topological Collections, Transformations and Their Application to the Modeling and the Simulation of Dynamical Systems. In: Nieuwenhuis, R. (eds) Rewriting Techniques and Applications. RTA 2003. Lecture Notes in Computer Science, vol 2706. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44881-0_16

Download citation

  • DOI: https://doi.org/10.1007/3-540-44881-0_16

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40254-1

  • Online ISBN: 978-3-540-44881-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation