Skip to main content
SpringerLink
Log in

Probing robustness of cellular automata through variations of asynchronous updating

Natural Computing volume 11, pages 553–564 (2012)Cite this article

Abstract

Typically viewed as a deterministic model of spatial computing, cellular automata are here considered as a collective system subject to the noise inherent to natural computing. The classical updating scheme is replaced by stochastic versions which either randomly update cells or disrupt the cell-to-cell transmission of information. We then use the novel updating schemes to probe the behaviour of elementary cellular automata, and observe a wide variety of results. We study these behaviours in the scope of macroscopic statistical phenomena and microscopic analysis. Finally, we discuss the possibility to use updating schemes to probe the robustness of complex systems.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price includes VAT (Canada)

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Notes

  1. Because of the proximity of their definitions, the effects of β- and γ-synchronism on CA behaviours are expected to be similar in most cases. Therefore γ-synchronism will only be mentioned when a difference with β-synchronism is observed.

  2. The complete set of results can be found at: http://www.loria.fr/~boure/eca.

  3. For the sake of conciseness, we choose to put the third class DP2 aside, as it displays a phase transition in ECA 178, but for an order parameter different than density.

References

  • Ackley DH, Williams LR (2011) Homeostatic architecture for robust spatial computing. In: Proceedings of the 5th IEEE international conference on self-adaptive and self-organizing systems

  • Bandini S, Bonomi A, Vizzari G (2010) What do we mean by asynchronous CA? A reflection on types and effects of asynchronicity. In: Proceedings of ACRI 2010. Lecture notes in computer science, vol 6350, pp 385–394

  • Bandini S, Bonomi A, Vizzari G (2010) Modeling and programming asynchronous automata networks: the MOCA approach. In: Proceedings of ACRI 2010. Lecture notes in computer science, vol 6350, pp 345–355

  • Blok HJ, Bergersen B (1999) Synchronous versus asynchronous updating in the "Game of Life”. Phys Rev E 590(4):3876–3879

    Article  Google Scholar 

  • Bouré O, Fatès N, Chevrier V (2011) Robustness of cellular automata in the light of asynchronous information transmission. In Unconventional Computation, volume 6714 of Lecture Notes in Computer Science, pp 52–63

  • Bouré O, Fatès N, Chevrier V (2012) First steps on asynchronous lattice-gas models with an application to a swarming rule. In: Proceedings of ACRI 2012. Lecture notes in computer science. http://hal.inria.fr/hal-00687987/ (to appear)

  • Culik K II, Yu S (1988) Undecidability of CA classification schemes. Complex Syst 2:177–190

    MathSciNet  MATH  Google Scholar 

  • Fatès N (2009) Asynchronism induces second order phase transitions in elementary cellular automata. J Cell Autom 40(1):21–38

    Google Scholar 

  • Fatès N (2010) Does Life resist asynchrony? In: Game of life cellular automata. Springer, London, pp 257–274

  • Fatès N, Morvan M (2005) An experimental study of robustness to asynchronism for elementary cellular automata. Complex Syst 16:1–27

    Google Scholar 

  • Fukś H, Skelton A (2012) Orbits of bernoulli measure in asynchronous cellular automata. DMTCS, AP:0, pp 95–112. In: Proceedings of automata 2011.

  • Gouaïch A, Michel F, Guiraud Y (2005) MIC*: a deployment environment for autonomous agents. In: Post-proceedings of the 1st international workshop in environments for multiagent systems. Springer, London, , pp 109–126

  • Grilo C, Correia L (2011) Effects of asynchronism on evolutionary games. J Theor Biol 2690(1):109–122

    Article  Google Scholar 

  • Hinrichsen H (2000) Nonequilibrium critical phenomena and phase transitions into absorbing states. Adv Phys 49:815–958

    Article  Google Scholar 

  • Ingerson TE, Buvel RL (1984) Structure in asynchronous cellular automata. Physica D 100(1–2):59–68

    Article  MathSciNet  Google Scholar 

  • Peper F, Isokawa T, Takada Y, Matsui N (2002) Self-timed cellular automata and their computational ability. Futur Gener Comput Syst 180(7):893–904

    Article  Google Scholar 

  • Regnault D (2008) Directed percolation arising in stochastic cellular automata analysis. In: Mathematical foundations of computer science. Lecture notes in computer science, vol 5162. Springer, London, pp 563–574

  • von Neumann J (1966) Theory of self-reproducing automata. University of Illinois Press, Champaign

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université de Lorraine—INRIA Nancy Grand-Est—LORIA, Nancy, France

    Olivier Bouré, Nazim Fatès & Vincent Chevrier

Authors
  1. Olivier Bouré
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nazim Fatès
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vincent Chevrier
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Olivier Bouré.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bouré, O., Fatès, N. & Chevrier, V. Probing robustness of cellular automata through variations of asynchronous updating. Nat Comput 11, 553–564 (2012). https://doi.org/10.1007/s11047-012-9340-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11047-012-9340-y

Keywords

  • Asynchronous cellular automata
  • Robustness
  • Discrete dynamical systems
  • Phase transitions
  • Directed percolation

Search

Navigation