Dynamics and Self-Organization in One-Dimensional Arrays

  • Maurice Tchuente
Conference paper
Part of the NATO ASI Series book series (volume 20)

Abstract

A one-dimensional (1-D for short) array is a collection of identical finite state machines indexed by integers x of ℤ, and where any cell x can directly receive informations from its neighbours x + i, i = -n,…, n, where n is a positive integer called the scope of the array. Each machine can synchronously change its state at discrete time steps as a function of its state and the states of its neighboring machines.

Keywords

OLIVOS TMse 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. BALZER R. (1967): An 8-state minimal time solution to the Firing Squad Synchronization Problem. Information and Control, 10, pp 22–42CrossRefGoogle Scholar
  2. CONWAY J. (1970): Mathematical games, Scientific American, pp 120–123 (paper written by M. GARDNER)Google Scholar
  3. DIJKSTRA E.W. (1974): Self-stabilizing systems in spite of distributed control, Communications of the ACM, (17), 11, pp 643–644CrossRefGoogle Scholar
  4. FOGELMAN SOULIE F. (1985) Contribution à une théorie du calcul sur réseaux, Thèse d’état, USMG-INPG, GrenobleGoogle Scholar
  5. GOLES E. and OLIVOS J. (1980): Comportement itératif des fonctions à multiseuil, Information and Control, (45), (3), pp 300–313CrossRefMATHMathSciNetGoogle Scholar
  6. GOLES E. and TCHUENTE M. (1984): Iterative behaviour of one-dimensional threshold automata, Discrete Applied Mathematics, 8, pp 319–322CrossRefMATHMathSciNetGoogle Scholar
  7. GOLES E. (1985): Comportement dynamique de réseaux d’automates, Thèse d’état, USMG-INPG, Grenoble.Google Scholar
  8. ROBERT F. (1985): Discrete Iterations, Academic Press, to appear.Google Scholar
  9. ROMANI F. (1976): Cellular automata synchronization, Information Sciences, 10, pp 299–318Google Scholar
  10. ROSENSTIEHL P. (1966): Existence d’automates d’états finis capables de s’accorder bien qu’arbitrairement connectés et nombreux, International Computation Centre Bulletin, 5, pp 215–244Google Scholar
  11. TCHUENTE M. (1977): Evolution de certains automates cellulaires uniformes binaires à seuil, Séminaire d’Analyse numérique, 265, GrenobleGoogle Scholar
  12. TCHUENTE M. (1981): Sur l’auto-stabilisation dans un réseau d’ordinateurs, RAIRO Theoretical Computer Science, (15), 1, pp 47–66MATHMathSciNetGoogle Scholar
  13. TCHUENTE M. (1982): Contribution à l’étude des méthodes de calcul pour des systèmes de type coopératif, Thèse d’état, USMG-INPG, GrenobleGoogle Scholar
  14. UNGER S.H. (1959): Pattern detection and recognition, Proc. IRE, pp 1737–1752Google Scholar
  15. VON NEUMANN J. (1966): Theory of Self-Reproducing Automata, A.W. BURKS ed., University of Illinois Press.Google Scholar
  16. WAKSMAN A. (1966): An optimum solution to the firing squad synchronization problem, Information and Control, 9, pp 66–78CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Maurice Tchuente
    • 1
  1. 1.CNRS-IMAG Laboratoire TIM3Saint Martin d’Hères cédexFrance

Personalised recommendations