Advertisement

Computations in Space and Space in Computations

  • Jean-Louis Giavitto
  • Olivier Michel
  • Julien Cohen
  • Antoine Spicher
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3566)

Abstract

The emergence of terms like natural computing, mimetic computing, parallel problem solving from nature, bio-inspired computing, neurocomputing, evolutionary computing, etc., shows the never ending interest of the computer scientists for the use of “natural phenomena” as “problem solving devices” or more generally, as a fruitful source of inspiration to develop new programming paradigms. It is the latter topic which interests us here. The idea of numerical experiment can be reversed and, instead of using computers to simulate a fragment of the real world, the idea is to use (a digital simulation of) the real world to compute. In this perspective, the processes that take place in the real world are the objects of a new calculus:

description of the world’s laws = program

state of the world = data of the program

parameters of the description = inputs of the program

simulation = the computation

Keywords

Cellular Automaton Cellular Automaton Cayley Graph Hamiltonian Path Evolution Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arulanandham, J., Calude, C., Dinneen, M.: Bead-sort: A natural sorting algorithm. Bulletin of the European Association for Theoretical Computer Science 76, 153–162 (2002) (Technical Contributions)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Banatre, J.-P., Coutant, A., Metayer, D.L.: A parallel machine for multiset transformation and its programming style. Future Generation Computer Systems 4, 133–144 (1988)CrossRefGoogle Scholar
  3. 3.
    Banâtre, J.-P., Fradet, P., Métayer, D.L.: Gamma and the chemical reaction model: Fifteen years after. In: Calude, C.S., Pun, G., Rozenberg, G., Salomaa, A. (eds.) Multiset Processing. LNCS, vol. 2235, pp. 17–44. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Berry, G., Boudol, G.: The chemical abstract machine. In: Conf. Record 17th ACM Symp. on Principles of Programmming Languages, POPL 1990, San Francisco, CA, USA, January 17-19, 1990, pp. 81–94. ACM Press, New York (1990)CrossRefGoogle Scholar
  5. 5.
    Brockett, R.W.: Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems. Linear Algebra and its Applications 146, 79–91 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Chandy, K.M.: Reasoning about continuous systems. Science of Computer Programming 14(2–3), 117–132 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Coffman, E.G., Elphick, M.J., Shoshani, A.: System deadlocks. Computing Surveys 3(2), 67–78 (1971)zbMATHCrossRefGoogle Scholar
  8. 8.
    Cohen, J.: Typing rule-based transformations over topological collections. In: Giavitto, J.-L., Moreau, P.-E. (eds.) 4th International Workshop on Rule-Based Programming (RULE 2003), pp. 50–66 (2003)Google Scholar
  9. 9.
    Cohen, J.: Typage fort et typage souple des collections topologiques et des transformations. In: Ménissier-Morain, V. (ed.) Journées Francophones des Langages Applicatifs (JFLA 2004), pp. 37–54, INRIA (2004) Google Scholar
  10. 10.
    Fradet, P., Métayer, D.L.: Structured Gamma. Science of Computer Programming 31(2–3), 263–289 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Fradet, P., Métayer, D.L.: Shape types. In: Proc. of Principles of Programming Languages, Paris, France, January 1997. ACM Press, New York (1997)Google Scholar
  12. 12.
    Geurts, F.: Hierarchy of discrete-time dynamical systems, a survey. Bulletin of the European Association for Theoretical Computer Science 57, 230–251 (1995) (Surveys and Tutorials)zbMATHGoogle Scholar
  13. 13.
    Giavitto, J.-L.: A framework for the recursive definition of data structures. In: ACM-Sigplan 2nd International Conference on Principles and Practice of Declarative Programming (PPDP 2000), Montréal, September 2000, pp. 45–55. ACM press, New York (2000)CrossRefGoogle Scholar
  14. 14.
    Giavitto, J.-L.: Invited talk: Topological collections, transformations and their application to the modeling and the simulation of dynamical systems. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 208–233. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  15. 15.
    Giavitto, J.-L., Godin, C., Michel, O., Prusinkiewicz, P.: Computational Models for Integrative and Developmental Biology. In: Modelling and Simulation of biological processes in the context of genomics, Hermes (July 2002) (Also republished as an high-level course in the proceedings of the Dieppe spring school on Modelling and simulation of biological processes in the context of genomics, May 12-17, 2003, Dieppes, France)Google Scholar
  16. 16.
    Giavitto, J.-L., Michel, O.: Declarative definition of group indexed data structures and approximation of their domains. In: Proceedings of the 3rd International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming (PPDP 2001), September 2001, ACM Press, New York (2001)Google Scholar
  17. 17.
    Giavitto, J.-L., Michel, O.: Mgs: a rule-based programming language for complex objects and collections. In: van den Brand, M., Verma, R. (eds.) Electronic Notes in Theoretical Computer Science, vol. 59. Elsevier Science, Amsterdam (2001)Google Scholar
  18. 18.
    Giavitto, J.-L., Michel, O.: 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. 19.
    Giavitto, J.-L., Michel, O.: Data structure as topological spaces. In: Calude, C.S., Dinneen, M.J., Peper, F. (eds.) UMC 2002. LNCS, vol. 2509, pp. 137–150. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  20. 20.
    Giavitto, J.-L., Michel, O.: The topological structures of membrane computing. Fundamenta Informaticae 49, 107–129 (2002)MathSciNetGoogle Scholar
  21. 21.
    Giavitto, J.-L., Michel, O., Sansonnet, J.-P.: Group based fields. In: Queinnec, C., Halstead Jr., R.H., Ito, T. (eds.) PSLS 1995. LNCS, vol. 1068, pp. 209–215. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  22. 22.
    Goubault, E.: Geometry and concurrency: A user’s guide. Mathematical Structures in Computer Science 10, 411–425 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Granger, G.-G.: La pensée de l’espace. Odile Jacob (1999)Google Scholar
  24. 24.
    Henle, M.: A combinatorial introduction to topology. Dover publications, Mineola (1994)zbMATHGoogle Scholar
  25. 25.
    Jay, C.B.: A semantics for shape. Science of Computer Programming 25(2–3), 251–283 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Jeuring, J., Jansson, P.: AFP 1996. LNCS, vol. 1129, pp. 68–114 (1996)Google Scholar
  27. 27.
    Lienhardt, P.: Topological models for boundary representation: a comparison with n-dimensional generalized maps. Computer-Aided Design 23(1), 59–82 (1991)zbMATHCrossRefGoogle Scholar
  28. 28.
    Lindenmayer, A.: Mathematical models for cellular interaction in development, Parts I and II. Journal of Theoretical Biology 18, 280–315 (1968)CrossRefGoogle Scholar
  29. 29.
    Meijer, E., Fokkinga, M., Paterson, R.: Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire. In: Hughes, J. (ed.) FPCA 1991. LNCS, vol. 523, pp. 124–144. Springer, Heidelberg (1991)Google Scholar
  30. 30.
    Michel, O., Jacquemard, F.: An Analysis of a Public-Key Protocol with Membranes. Natural Computing Series, pp. 281–300. Springer, Heidelberg (2005)Google Scholar
  31. 31.
    Paun, G.: From cells to computers: Computing with membranes (P systems). Biosystems 59(3), 139–158 (2001)CrossRefGoogle Scholar
  32. 32.
    Prusinkiewicz, P., Hanan, J.: L systems: from formalism to programming languages. In: Ronzenberg, G., Salomaa, A. (eds.) Lindenmayer Systems, Impacts on Theoretical Computer Science, Computer Graphics and Developmental Biology, Febraury 1992, pp. 193–211. Springer, Heidelberg (1992)Google Scholar
  33. 33.
    Róka, Z.: One-way cellular automata on Cayley graphs. Theoretical Computer Science 132(1–2), 259–290 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    Sintzoff, M.: Invariance and contraction by infinite iterations of relations. In: Research directions in high-level programming languages, Mont Saint-Michel, France, June 1991. LNCS, vol. 574, pp. 349–373. Springer, Heidelberg (1991)Google Scholar
  35. 35.
    Sorkin, R.D.: A finitary substitute for continuous topology. Int. J. Theor. Phys. 30, 923–948 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  36. 36.
    Spicher, A., Michel, O., Giavitto, J.-L.: A topological framework for the specification and the simulation of discrete dynamical systems. In: Sloot, P.M.A., Chopard, B., Hoekstra, A.G. (eds.) ACRI 2004. LNCS, vol. 3305, pp. 238–247. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  37. 37.
    The MAUDE project. Maude home page (2002), http://maude.csl.sri.com/
  38. 38.
    The PROTHEO project. Elan home page (2002), http://www.loria.fr/equipes/protheo/SOFTWARES/ELAN/
  39. 39.
    Weyl, H.: The Classical Groups (their invariants and representations). Princeton University Press, Princeton (1939); Reprint edition (October 13, 1997) ISBN 0691057567Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jean-Louis Giavitto
    • 1
  • Olivier Michel
    • 1
  • Julien Cohen
    • 1
  • Antoine Spicher
    • 1
  1. 1.LaMI, umr 8042 du CNRSUniversité d’ÉvryÉvryFrance

Personalised recommendations