Skip to main content

Scale-Free Automata Networks Are Not Robust in a Collective Computational Task

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4173))

Abstract

We investigate the performances and collective task-solving capabilities of complex networks of automata using the density problem as a typical case. We show by computer simulations that evolved Watts–Strogatz small-world networks have superior performance with respect to scale-free graphs of the Albert–Barabási type. Besides, Watts–Strogatz networks are much more robust in the face of transient uniformly random perturbations. This result differs from information diffusion on scale-free networks, where random faults are highly tolerated.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Newman, M.E.J.: The structure and function of complex networks. SIAM Review 45, 167–256 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393, 440–442 (1998)

    Article  Google Scholar 

  3. Garzon, M.: Models of Massive Parallelism: Analysis of Cellular Automata and Neural Networks. Springer, Berlin (1995)

    MATH  Google Scholar 

  4. Kauffman, S.A.: The Origins of Order. Oxford University Press, New York (1993)

    Google Scholar 

  5. Watts, D.J.: Small worlds: The Dynamics of Networks between Order and Randomness. Princeton University Press, Princeton NJ (1999)

    Google Scholar 

  6. 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)

    Chapter  Google Scholar 

  7. 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)

    Chapter  Google Scholar 

  8. Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Reviews of Modern Physics 74, 47–97 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. Land, M., Belew, R.K.: No perfect two-state cellular automata for density classification exists. Physical Review Letters 74(25), 5148–5150 (1995)

    Article  Google Scholar 

  10. Capcarrère, M.S., Sipper, M., Tomassini, M.: Two-state, r=1 cellular automaton that classifies density. Physical Review Letters 77(24), 4969–4971 (1996)

    Article  Google Scholar 

  11. Fukś, H.: Solution of the density classification problem with two cellular automata rules. Physical Review E 55(3), 2081–2084 (1997)

    Article  Google Scholar 

  12. 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 

  13. Tomassini, M., Giacobini, M., Darabos, C.: Evolution and dynamics of small-world cellular automata. Complex Systems 15, 261–284 (2005)

    MATH  MathSciNet  Google Scholar 

  14. Sipper, M., Tomassini, M., Beuret, O.: Studying probabilistic faults in evolved non-uniform cellular automata. International Journal of Modern Physics C 7(6), 923–939 (1996)

    Article  Google Scholar 

  15. Albert, R., Jeong, H., Barabási, L.: Error and attack tolerance of complex networks. Nature 406, 378–382 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Darabos, C., Giacobini, M., Tomassini, M. (2006). Scale-Free Automata Networks Are Not Robust in a Collective Computational Task. In: El Yacoubi, S., Chopard, B., Bandini, S. (eds) Cellular Automata. ACRI 2006. Lecture Notes in Computer Science, vol 4173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11861201_59

Download citation

  • DOI: https://doi.org/10.1007/11861201_59

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40929-8

  • Online ISBN: 978-3-540-40932-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics