Skip to main content

The Role of Conceptual Structure in Designing Cellular Automata to Perform Collective Computation

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5204))

Abstract

The notion of conceptual structure in CA rules that perform the density classification task (DCT) was introduced by [1]. Here we investigate the role of process-symmetry in CAs that solve the DCT, in particular the idea of conceptual similarity, which defines a novel search space for CA rules. We report on two new process-symmetric one-dimensional rules for the DCT which have the highest “balanced” performance observed to date on this task, as well as the highest-performing CA known to perform the DCT in two dimensions. Finally, we investigate the more general problem of assessing how different learning strategies (based on evolution and coevolution, with and without spatial distribution), previously compared by [2], are suited to exploit conceptual structure in learning CAs to perform collective computation.

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   74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   99.00
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. Marques-Pita, M., Manurung, R., Pain, H.: Conceptual representations: What do they have to say about the density classification task by cellular automata? In: Jost, J., Reed-Tsotchas, F., Schuster, P. (eds.) ECCS 2006. European Conference on Complex Systems (2006)

    Google Scholar 

  2. Mitchell, M., Thomure, M.D., Williams, N.L.: The role of space in the success of coevolutionary learning. In: Proceedings of Artificial Life X: Tenth Annual Conference on the Simulation and Synthesis of Living Systems (2006)

    Google Scholar 

  3. Zhirnov, V., Cavin, R., Lemming, G., Galatsis, K.: An assessment of integrated digital cellular automata architectures. Computer 41(1), 38–44 (2008)

    Article  Google Scholar 

  4. Mitchell, M., Crutchfield, J., Hraber, P.: Revisiting the edge of chaos: Evolving cellular automata to perform computations. Complex Systems 7, 89–130 (1993)

    MATH  Google Scholar 

  5. Gacs, P., Kurdyumov, L., Levin, L.: One-dimensional uniform arrays that wash out finite islands. Probl. Peredachi. Inform. 14, 92–98 (1978)

    Google Scholar 

  6. Gonzaga de Sá, P., Maes, C.: Gacs-Kurdyumov-Levin automaton revisited. Journal of Statistical Physics 67(3-4), 507–522 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  7. Andre, D., Bennett III, F., Koza, J.: Discovery by genetic programming of a cellular automata rule that is better than any known rule for the majority classification problem. In: Koza, J., Goldberg, D., Fogel, D. (eds.) Proceedings of the First Annual Conference on Genetic Programming, pp. 3–11. MIT Press, Cambridge (1996)

    Google Scholar 

  8. Das, R., Mitchell, M., Crutchfield, J.: A genetic algorithm discovers particle-based computation in cellular automata. In: Davidor, Y., Schwefel, H.P., Männer, R. (eds.) Proceedings of the Int.Conf. on Evolutionary Computation, pp. 344–353 (1994)

    Google Scholar 

  9. Juillé, H., Pollack, B.: Coevolving the ideal trainer: Application to discovery of cellular automata rules. In: Garzon, M.H., Goldberg, D.E., Iba, H., Riolo, R. (eds.) Genetic Programming 1998: Proceedings of the Third Annual Conference. Morgan Kaufmann, San Francisco (1998)

    Google Scholar 

  10. Ferreira, C.: Gene expression programming: A new adapive algorithm for solving problems. Complex Systems 13(2), 87–129 (2001)

    MathSciNet  Google Scholar 

  11. Karmiloff-Smith, A.: Beyond Modularity: A Developmental Perspective on Cognitive Science. MIT Press, Cambridge (1992)

    Google Scholar 

  12. Gärdenfors, P.: Conceptual Spaces: The Geometry of Tought. MIT Press/Bradford Books (2000)

    Google Scholar 

  13. Marques-Pita, M.: Aitana: A Developmental Cognitive Artifact to Explore the Evolution of Conceptual Representations of Cellular Automata-based Complex Systems. PhD thesis, School of Informatics, University of Edinburgh, Edinburgh, UK (2006)

    Google Scholar 

  14. Holland, J., Holyoak, K., Nisbett, R., Thagard, P.: Induction: Processes of Inference, Learning and Discovery. MIT Press, Cambridge (1986)

    Google Scholar 

  15. Piaget, J.: The Origins of Intelligence in Children. International University Press (1952)

    Google Scholar 

  16. Piaget, J.: The Child’s Construction of Reality. Routledge and Kegan Paul (1955)

    Google Scholar 

  17. Marques-Pita, M., Rocha, L.M.: Conceptual structure in cellular automata: The density classification task. In: Bullock, S., Noble, J., Watson, R.A., Bedau, M.A. (eds.) Proceedings of the Eleventh International Conference on Artificial Life (Alife XI). MIT Press, Cambridge (2008)

    Google Scholar 

  18. Crutchfield, J.P., Mitchell, M., Das, R.: The evolutionary design of collective computation in cellular automata. In: Crutchfield, J.P., Schuster, P.K. (eds.) Evolutionary Dynamics—Exploring the Interplay of Selection, Neutrality, Accident, and Function, pp. 361–411. Oxford University Press, New York (2003)

    Google Scholar 

  19. Woltz, D., De Oliveira, P.: Very effective evolutionary techniques for searching cellular automata rule spaces. Journal of Cellular Automata (to appear)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Cristian S. Calude José Félix Costa Rudolf Freund Marion Oswald Grzegorz Rozenberg

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Marques-Pita, M., Mitchell, M., Rocha, L.M. (2008). The Role of Conceptual Structure in Designing Cellular Automata to Perform Collective Computation. In: Calude, C.S., Costa, J.F., Freund, R., Oswald, M., Rozenberg, G. (eds) Unconventional Computing. UC 2008. Lecture Notes in Computer Science, vol 5204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85194-3_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85194-3_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85193-6

  • Online ISBN: 978-3-540-85194-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics