Generalized Automata Networks

  • Marco Tomassini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4173)


In this work standard lattice cellular automata and random Boolean networks are extended to a wider class of generalized automata networks having any graph topology as a support. Dynamical, computational, and problem solving capabilities of these automata networks are then discussed through selected examples, and put into perspective with respect to current and future research.


Cellular Automaton Random Graph Cellular Automaton Boolean Network Genetic Regulatory Network 
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.


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  1. 1.
    Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Reviews of Modern Physics 74, 47–97 (2002)CrossRefMathSciNetMATHGoogle Scholar
  2. 2.
    Albert, R., Jeong, H., Barabási, L.: Error and attack tolerance of complex networks. Nature 406, 378–382 (2000)CrossRefGoogle Scholar
  3. 3.
    Aldana, M.: Boolean dynamics of networks with scale-free topology. Physica D 185, 45–66 (2003)CrossRefMathSciNetMATHGoogle Scholar
  4. 4.
    Amaral, L.A.N., Díaz-Guilera, A., Moreira, A., Goldberger, A.L., Lipsitz, L.A.: Emergence of complex dynamics in a simple model of signaling networks. Proc. Nat. Acad. Sci. USA 101(44), 15551–15555 (2004)CrossRefMATHGoogle Scholar
  5. 5.
    Capcarrère, M.S., Sipper, M., Tomassini, M.: Two-state, r=1 cellular automaton that classifies density. Physical Review Letters 77(24), 4969–4971 (1996)CrossRefGoogle Scholar
  6. 6.
    Chopard, B., Droz, M.: Cellular Automata Modeling of Physical Systems. Cambridge University Press, Cambridge (1998)CrossRefMATHGoogle Scholar
  7. 7.
    Crutchfield, J.P., Mitchell, M., Das, R.: Evolutionary design of collective computation in cellular automata. In: Crutchfield, J.P., Schuster, P. (eds.) Evolutionary Dynamics: Exploring the Interplay of Selection, Accident, Neutrality, and Function, pp. 361–411. Oxford University Press, Oxford (2003)Google Scholar
  8. 8.
    Darabos, C., Giacobini, M., Tomassini, M.: Scale-free automata networks are not robust in a collective computational task. In: El Yacoubi, S., Chopard, B., Bandini, S. (eds.) ACRI 2006. LNCS, vol. 4173, Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Das, R., Mitchell, M., Crutchfield, J.P.: A genetic algorithm discovers particle-based computation in cellular automata. In: Davidor, Y., Männer, R., Schwefel, H.-P. (eds.) PPSN 1994. LNCS, vol. 866, pp. 344–353. Springer, Heidelberg (1994)Google Scholar
  10. 10.
    Davidson, E.H., et al.: A genomic regulatory network for development. Science 295, 1669–1678 (2002)CrossRefGoogle Scholar
  11. 11.
    Fukś, H.: Solution of the density classification problem with two cellular automata rules. Physical Review E 55(3), 2081–2084 (1997)CrossRefGoogle Scholar
  12. 12.
    Garzon, M.: Models of Massive Parallelism: Analysis of Cellular Automata and Neural Networks. Springer, Berlin (1995)MATHGoogle Scholar
  13. 13.
    Giacobini, M., Tomassini, M., De Los Rios, P., Pestelacci, E.: Dynamics of scale-free semi-synchronous boolean networks. In: Rocha, L.M., et al. (eds.) Artificial Life X, pp. 1–7. MIT Press, Cambridge (2006)Google Scholar
  14. 14.
    Harvey, I., Bossomaier, T.: Time out of joint: attractors in asynchronous random boolean networks. In: Husbands, P., Harvey, I. (eds.) Proceedings of the Fourth European Conference on Artificial Life, pp. 67–75. MIT Press, Cambridge (1997)Google Scholar
  15. 15.
    Kauffman, S.A.: Metabolic stability and epigenesis in randomly constructed genetic nets. Journal of Theoretical Biology 22, 437–467 (1969)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Kauffman, S.A.: The Origins of Order. Oxford University Press, New York (1993)Google Scholar
  17. 17.
    Land, M., Belew, R.K.: No perfect two-state cellular automata for density classification exists. Physical Review Letters 74(25), 5148–5150 (1995)CrossRefGoogle Scholar
  18. 18.
    Langton, C.G.: Computation at the edge of chaos: Phase transitions and emergent computation. Physica D 42, 12–37 (1990)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Marr, C., Hütt, M.-T.: Topology regulates pattern formation capacity of binary cellular automata on graphs. Physica A 354, 641–662 (2005)CrossRefGoogle Scholar
  20. 20.
    Mesot, B., Teuscher, C.: Critical values in asynchronous random boolean networks. In: Banzhaf, W., Ziegler, J., Christaller, T., Dittrich, P., Kim, J.T. (eds.) ECAL 2003. LNCS (LNAI), vol. 2801, pp. 367–376. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  21. 21.
    Mesot, B., Teuscher, C.: Deducing local rules for solving global tasks with random Boolean networks. Physica D 211, 88–106 (2005)CrossRefMathSciNetMATHGoogle Scholar
  22. 22.
    Newman, M.E.J.: The structure and function of complex networks. SIAM Review 45, 167–256 (2003)CrossRefMathSciNetMATHGoogle Scholar
  23. 23.
    Pastor-Satorras, R., Vespignani, A.: Epidemic spreading in scale-free networks. Phy. Rev. Lett. 86, 3200–3203 (2001)CrossRefGoogle Scholar
  24. 24.
    Serra, R., Villani, M.: Perturbing the regular topology of cellular automata: implications for the dynamics. In: Bandini, S., Chopard, B., Tomassini, M. (eds.) ACRI 2002. LNCS, vol. 2493, pp. 168–177. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  25. 25.
    Sipper, M.: Evolution of Parallel Cellular Machines: The Cellular Programming Approach. Springer, Heidelberg (1997)Google Scholar
  26. 26.
    Sipper, M., Ruppin, E.: Co-evolving architectures for cellular machines. Physica D 99, 428–441 (1997)CrossRefMATHGoogle Scholar
  27. 27.
    Tomassini, M., Giacobini, M., Darabos, C.: Evolution of small-world networks of automata for computation. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 672–681. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  28. 28.
    Tomassini, M., Giacobini, M., Darabos, C.: Evolution and dynamics of small-world cellular automata. Complex Systems 15, 261–284 (2005)MathSciNetMATHGoogle Scholar
  29. 29.
    Vázquez, A., Dobrin, R., Sergi, D., Eckmann, J.-P., Oltvai, Z.N., Barabàsi, A.-L.: The topological relationships between the large-scale attributes and local interactions patterns of complex networks. Proc. Natl. Acad. Sci USA 101(52), 17940–17945 (2004)CrossRefGoogle Scholar
  30. 30.
    Watts, D.J.: Small worlds: The Dynamics of Networks between Order and Randomness. Princeton University Press, Princeton (1999)Google Scholar
  31. 31.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393, 440–442 (1998)CrossRefGoogle Scholar
  32. 32.
    Wolfram, S.: Universality and complexity in cellular automata. Physica D 10, 1–35 (1984)CrossRefMathSciNetGoogle Scholar
  33. 33.
    Wolfram, S.: A New Kind of Science. Wolfram Media (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Marco Tomassini
    • 1
  1. 1.Information Systems DepartmentUniversity of LausanneSwitzerland

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