Skip to main content
SpringerLink
Log in

Synchronisation of Elementary Cellular Automata with a Small Initial Error. Application to Rule 18

  • Conference paper
  • First Online:
Cellular Automata (ACRI 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13402))

  • 501 Accesses

Abstract

In this paper, we study how synchronization and state estimation are related in the context of elementary cellular automata. We first characterize the synchronization error between two 1D elementary cellular automata implementing Wolfram’s 18th rule. Then we propose a simple approach to statistically model the transient phase of the synchronization error spread. We finally present a way to utilize this model of the error spread to place mobile sensors in order to reduce the overall synchronization error when the initial error is small.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
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

Institutional subscriptions

References

  1. Bagnoli, F., Rechtman, R.: Synchronization and maximum Lyapunov exponents of cellular automata. Phys. Rev. E 59(2), R1307 (1999)

    Article  Google Scholar 

  2. Dogaru, R., Dogaru, I., Kim, H.: Binary chaos synchronization in elementary cellular automata. Int. J. Bifurc. Chaos 19(09), 2871–2884 (2009)

    Article  MathSciNet  Google Scholar 

  3. Dridi, S., Bagnoli, F., Yacoubi, S.E.: Markov chains approach for regional controllability of deterministic cellular automata, via boundary actions. J. Cell. Autom. 14(5/6), 479–498 (2019)

    MathSciNet  MATH  Google Scholar 

  4. El Yacoubi, S., Plénet, T., Dridi, S., Bagnoli, F., Lefèvre, L., Raïevsky, C.: Some control and observation issues in cellular automata. Complex Syst. 30(3), 391–413 (2021)

    Article  Google Scholar 

  5. Kalman, R.E.: Mathematical description of linear dynamical systems. J. Soc. Ind. Appl. Math. Ser. A Control 1(2), 152–192 (1963)

    Article  MathSciNet  Google Scholar 

  6. Plénet, T., El Yacoubi, S., Raïevsky, C., Lefèvre, L.: Observability and reconstructibility of bounded cellular automata. Int. J. Syst. Sci., 1–17 (2022). https://doi.org/10.1080/00207721.2022.2064556

  7. Sarachik, P., Kreindler, E.: Controllability and observability of linear discrete-time systems. Int. J. Control 1(5), 419–432 (1965)

    Article  MathSciNet  Google Scholar 

  8. Urıas, J., Salazar, G., Ugalde, E.: Synchronization of cellular automaton pairs. Chaos Interdiscip. J. Nonlinear Sci. 8(4), 814–818 (1998)

    Article  MathSciNet  Google Scholar 

  9. Wolfram, S.: Universality and complexity in cellular automata. Physica D 10(1–2), 1–35 (1984)

    Article  MathSciNet  Google Scholar 

  10. Zhu, Q., Liu, Y., Lu, J., Cao, J.: Observability of Boolean control networks. Sci. China Inf. Sci. 61(9), 1–12 (2018)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Images UMR Espace-Dev, University of Perpignan via Domitia, Perpignan, France

    Théo Plénet & Samira El Yacoubi

  2. Univ. Grenoble Alpes, Grenoble INP, LCIS, 26000, Valence, France

    Clément Raïevsky & Laurent Lefèvre

  3. Physics and Astronomy and CSDC, University of Florence, Florence, Italy

    Franco Bagnoli

Authors
  1. Théo Plénet
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Samira El Yacoubi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Clément Raïevsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Laurent Lefèvre
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Franco Bagnoli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Théo Plénet .

Editor information

Editors and Affiliations

  1. University of Geneva, Geneva, Switzerland

    Bastien Chopard

  2. University of Milano-Bicocca, Milan, Italy

    Stefania Bandini

  3. University of Milano-Bicocca, Milan, Italy

    Alberto Dennunzio

  4. University of Geneva, Geneva, Switzerland

    Mira Arabi Haddad

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Plénet, T., El Yacoubi, S., Raïevsky, C., Lefèvre, L., Bagnoli, F. (2022). Synchronisation of Elementary Cellular Automata with a Small Initial Error. Application to Rule 18. In: Chopard, B., Bandini, S., Dennunzio, A., Arabi Haddad, M. (eds) Cellular Automata. ACRI 2022. Lecture Notes in Computer Science, vol 13402. Springer, Cham. https://doi.org/10.1007/978-3-031-14926-9_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-14926-9_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-14925-2

  • Online ISBN: 978-3-031-14926-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation