Abstract
In this paper, we study how synchronization and state estimation are related in the context of elementary cellular automata. We first characterize the geometric properties of the synchronization error between two replicas of a 1D elementary cellular automata following Wolfram’s rule 18. We propose a simple approach to statistically model the transient phase of the spreading of the synchronization error. We finally present a way to utilize our model of the error spreading to place mobile sensors in order to improve the overall replica synchronization in the case in which the initial error is small.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Data and materials availability
source codes and numerical simulation results are available on request from the corresponding author
References
Bagnoli F, Rechtman R (1999) Synchronization and maximum Lyapunov exponents of cellular automata. Phys Rev E 59(2):1307. https://doi.org/10.1103/PhysRevE.59.R1307
Bagnoli F, Rechtman R (2018) Regional synchronization of a probabilistic cellular automaton. In: Cellular Automata, Proceedings of 13th International Conference on Cellular Automata for Research and Industry, ACRI 2018, Como, Italy, September 17-21, 2018; LNTCS, Vol 11115, pp. 255–263. Springer, Switzerland. https://doi.org/10.1007/978-3-319-99813-8_23
Dogaru R, Dogaru I, Kim H (2009) Binary chaos synchronization in elementary cellular automata. Int J Bifurc Chaos 19(09):2871–2884. https://doi.org/10.1142/S0218127409024529
Dridi S, Bagnoli F, Yacoubi SE (2019) Markov chains approach for regional controllability of deterministic cellular automata, via boundary actions. J Cell Autom 14(5/6):479–498
El Yacoubi S, Plénet T, Dridi S, Bagnoli F, Lefèvre L, Raïevsky C (2021) Some control and observation issues in cellular automata. Complex Syst 30(3):391–413. https://doi.org/10.25088/ComplexSystems.30.3.391
Kalman RE (1963) Mathematical description of linear dynamical systems. J Soc Ind Appl Math, Ser A: Control 1(2):152–192. https://doi.org/10.1137/0301010
Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821–824. https://doi.org/10.1103/physrevlett.64.821
Pecora LM, Carroll TL (2015) Synchronization of chaotic systems. Chaos: Interdiscip J Nonlinear Sci 25(9):097611. https://doi.org/10.1063/1.4917383
Plénet T, Raïevsky C, Lefèvre L, El Yacoubi S (2020) Social organisation of mobile sensors for wildfire spread estimation. IFAC-PapersOnLine 53(2):3596–3601. https://doi.org/10.1016/j.ifacol.2020.12.2545
Plénet T, El Yacoubi S, Raïevsky C, Lefèvre L (2022) Observability and reconstructibility of bounded cellular automata. Int J Syst Sci. https://doi.org/10.1080/00207721.2022.2064556
Sarachik P, Kreindler E (1965) Controllability and observability of linear discrete-time systems. Int J Control 1(5):419–432. https://doi.org/10.1080/00207176508905497
Urıas J, Salazar G, Ugalde E (1998) Synchronization of cellular automaton pairs. Chaos: Interdiscip J Nonlinear Sci 8(4):814–818. https://doi.org/10.1063/1.166367
Wolfram S (1984) Universality and complexity in cellular automata. Physica D 10(1–2):1–35. https://doi.org/10.1016/0167-2789(84)90245-8
Zhu Q, Liu Y, Lu J, Cao J (2018) Observability of boolean control networks. Sci China Inf Sci 61(9):1–12. https://doi.org/10.1007/s11432-017-9135-4
Funding
Théo Plenet received a funding from the University of Perpignan Via Domitia for this work (PhD grant from Doctoral School 305)
Author information
Authors and Affiliations
Contributions
All authors contributed equally to this work and reviewed the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
there is no competing interests of any financial or personal nature
Ethical approval
Not applicable.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Plénet, T., Bagnoli, F., El Yacoubi, S. et al. Synchronization of elementary cellular automata. Nat Comput 23, 31–40 (2024). https://doi.org/10.1007/s11047-023-09962-1
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11047-023-09962-1