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Cellular Automata and Formulae on Monoids

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Cellular Automata (ACRI 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8751))

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Abstract

This paper studies cellular automata with binary states on monoids making use of formulae in propositional logic, instead of local functions. Also we prove that the multiplication of formulae, defined by monoid action, determines the composition of transition functions of CA. This result converts the reversibility of transition functions to the reversibility of formulae. Several examples of reversible formulae are illustrated. Finally, introducing the Stone topology on configuration spaces, we give a neat proof of Hedlund’s theorem for CA.

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References

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Author information

Authors and Affiliations

  1. Center for Fundamental Education, Kyushu Sangyo University, Fukuoka, 813-8503, Japan

    Toshikazu Ishida

  2. Faculty of Information Engineering, Fukuoka Institute of Technology, Fukuoka, 811-0295, Japan

    Shuichi Inokuchi

  3. Professor Emeritus, Kyushu University, Fukuoka, Japan

    Yasuo Kawahara

Authors
  1. Toshikazu Ishida
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  2. Shuichi Inokuchi
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  3. Yasuo Kawahara
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Editor information

Editors and Affiliations

  1. Dept. of Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059, Krakow, Poland

    Jarosław Wąs

  2. Dept. of Electrical and Computer Engineering, Democritus University of Thrace, 67100, Xanthi, Greece

    Georgios Ch. Sirakoulis

  3. CSAI - Complex Systems and Artificial Intelligence Research Center, University of Milano-Bicocca, 20126, Milan, Italy

    Stefania Bandini

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© 2014 Springer International Publishing Switzerland

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Ishida, T., Inokuchi, S., Kawahara, Y. (2014). Cellular Automata and Formulae on Monoids. In: Wąs, J., Sirakoulis, G.C., Bandini, S. (eds) Cellular Automata. ACRI 2014. Lecture Notes in Computer Science, vol 8751. Springer, Cham. https://doi.org/10.1007/978-3-319-11520-7_7

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  • DOI: https://doi.org/10.1007/978-3-319-11520-7_7

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11519-1

  • Online ISBN: 978-3-319-11520-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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