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International Conference on Cellular Automata

ACRI 2010: Cellular Automata pp 409–418Cite as

Coxeter Groups and Asynchronous Cellular Automata

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 6350)

Abstract

The dynamics group of an asynchronous cellular automaton (ACA) relates properties of its long term dynamics to the structure of Coxeter groups. The key mathematical feature connecting these diverse fields is involutions. Group-theoretic results in the latter domain may lead to insight about the dynamics in the former, and vice-versa. In this article, we highlight some central themes and common structures, and discuss novel approaches to some open and open-ended problems. We introduce the state automaton of an ACA, and show how the root automaton of a Coxeter group is essentially part of the state automaton of a related ACA.

Keywords

  • Conjugacy Class
  • Word Problem
  • Periodic Point
  • Coxeter Group
  • Vertex Function

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Clemson University, USA

    Matthew Macauley

  2. Department of Mathematics and NDSSL/VBI, Virginia Tech., USA

    Henning S. Mortveit

Authors
  1. Matthew Macauley
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  2. Henning S. Mortveit
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Editor information

Editors and Affiliations

  1. Complex Systems and Artificial Intelligence Research Center, University of Milano-Bicocca, Viale Sarca 336, Milano, Italy

    Stefania Bandini, Sara Manzoni & Giuseppe Vizzari,  & 

  2. University of Osaka Electro-Communication, 572-8530, Neyagawa, Osaka, Japan

    Hiroshi Umeo

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Macauley, M., Mortveit, H.S. (2010). Coxeter Groups and Asynchronous Cellular Automata. In: Bandini, S., Manzoni, S., Umeo, H., Vizzari, G. (eds) Cellular Automata. ACRI 2010. Lecture Notes in Computer Science, vol 6350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15979-4_43

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  • DOI: https://doi.org/10.1007/978-3-642-15979-4_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15978-7

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