Evolution of Small-World Networks of Automata for Computation

  • Marco Tomassini
  • Mario Giacobini
  • Christian Darabos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3242)

Abstract

We study an extension of cellular automata to arbitrary interconnection topologies for the majority problem. By using an evolutionary algorithm, we show that small-world network topologies consistently evolve from regular and random structures without being designed beforehand. These topologies have better performance than regular lattice structures and are easier to evolve, which could explain in part their ubiquity.

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References

  1. 1.
    Albert, R., Barabasi, A.-L.: Statistical mechanics of complex networks. Reviews of Modern Physics 74, 47–97 (2002)CrossRefMathSciNetMATHGoogle Scholar
  2. 2.
    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
  3. 3.
    Dorronsoro, B., Alba, E., Giacobini, M., Tomassini, M.: The influence of grid shape and asynchronicity in cellular evolutionary algorithms. In: Congress on Evolutionary Computation (CEC 2004) (to appear)Google Scholar
  4. 4.
    Garzon, M. (ed.): Models of Massive Parallelism: Analysis of Cellular Automata and Neural Networks. Springer, Berlin (1995)MATHGoogle Scholar
  5. 5.
    Kauffman, S.A.: The Origins of Order. Oxford University Press, New York (1993)Google Scholar
  6. 6.
    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
  7. 7.
    Thomson Leighton, F.: Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes. Morgan Kaufmann, San Mateo (1992)MATHGoogle Scholar
  8. 8.
    Mitchell, M., Crutchfield, J.P., Hraber, P.T.: Evolving cellular automata to perform computations: Mechanisms and impediments. Physica D 75, 361–391 (1994)MATHCrossRefGoogle Scholar
  9. 9.
    Mitchell, M., Hraber, P.T., Crutchfield, J.P.: Revisiting the edge of chaos: Evolving cellular automata to perform computations. Complex Systems 7, 89–130 (1993)MATHGoogle Scholar
  10. 10.
    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
  11. 11.
    Sipper, M.: Evolution of Parallel Cellular Machines: The Cellular Programming Approach. Springer, Heidelberg (1997)Google Scholar
  12. 12.
    Sipper, M., Ruppin, E.: Co-evolving architectures for cellular machines. Physica D 99, 428–441 (1997)MATHCrossRefGoogle Scholar
  13. 13.
    Watts, D.J.: Small worlds: The Dynamics of Networks between Order and Randomness. Princeton University Press, Princeton (1999)Google Scholar
  14. 14.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393, 440–442 (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Marco Tomassini
    • 1
  • Mario Giacobini
    • 1
  • Christian Darabos
    • 1
  1. 1.Information Systems DepartmentUniversity of LausanneSwitzerland

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