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Asymptotic (a)Synchronism Sensitivity and Complexity of Elementary Cellular Automata

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LATIN 2024: Theoretical Informatics (LATIN 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14579))

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Abstract

Among the fundamental questions in computer science is that of the impact of synchronism/asynchronism on computations, which has been addressed in various fields of the discipline: in programming, in networking, in concurrence theory, in artificial learning, etc. In this paper, we tackle this question from a standpoint which mixes discrete dynamical system theory and computational complexity, by highlighting that the chosen way of making local computations can have a drastic influence on the performed global computation itself. To do so, we study how distinct update schedules may fundamentally change the asymptotic behaviors of finite dynamical systems, by analyzing in particular their limit cycle maximal period. For the message itself to be general and impacting enough, we choose to focus on a “simple” computational model which prevents underlying systems from having too many intrinsic degrees of freedom, namely elementary cellular automata. More precisely, for elementary cellular automata rules which are neither too simple nor too complex (the problem should be meaningless for both), we show that update schedule changes can lead to significant computational complexity jumps (from constant to superpolynomial ones) in terms of their temporal asymptotes.

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Acknowledgments

The authors are thankful to projects ANR-18-CE40-0002 “FANs” (MRW, SS), ANID-FONDECYT 1200006 (EG), ANID-FONDECYT Postdoctorado 3220205 (MRW), MSCA-SE-101131549 “ACANCOS” (EG, IDL, MRW, SS), STIC AmSud 22-STIC-02 (EG, IDL, MRW, SS) for their funding.

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Authors and Affiliations

  1. Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Peñalolén, Chile

    Isabel Donoso Leiva, Eric Goles & Martín Ríos-Wilson

  2. Université Publique, Marseille, France

    Sylvain Sené

  3. Aix Marseille Univ, CNRS, LIS, Marseille, France

    Isabel Donoso Leiva & Sylvain Sené

Authors
  1. Isabel Donoso Leiva
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  2. Eric Goles
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  3. Martín Ríos-Wilson
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  4. Sylvain Sené
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Corresponding author

Correspondence to Martín Ríos-Wilson .

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Editors and Affiliations

  1. DIM-CMM, Universidad de Chile, Santiago, Chile

    José A. Soto

  2. Technical University of Munich, Munich, Germany

    Andreas Wiese

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Donoso Leiva, I., Goles, E., Ríos-Wilson, M., Sené, S. (2024). Asymptotic (a)Synchronism Sensitivity and Complexity of Elementary Cellular Automata. In: Soto, J.A., Wiese, A. (eds) LATIN 2024: Theoretical Informatics. LATIN 2024. Lecture Notes in Computer Science, vol 14579. Springer, Cham. https://doi.org/10.1007/978-3-031-55601-2_18

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  • DOI: https://doi.org/10.1007/978-3-031-55601-2_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-55600-5

  • Online ISBN: 978-3-031-55601-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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