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A universal Brownian cellular automaton with 3 states and 2 rules

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Abstract

This paper presents a 3-state asynchronous cellular automaton (CA) that requires merely two transition rules to achieve computational universality. This universality is achieved by implementing Priese’s delay-insensitive circuit elements, called the E-element and the K-element, on the cell space of a so-called Brownian CA, which is an asynchronous CA containing local configurations that conduct a random walk in the circuit topology.

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Authors and Affiliations

  1. Graduate School of Enginnering, University of Hyogo, Himeji, Hyogo, Japan

    Teijiro Isokawa, Koji Ono & Nobuyuki Matsui

  2. Center for Information and Neural Networks, National Institute of Information and Communications Technology, and Osaka University, Suita, Osaka, Japan

    Ferdinand Peper

Authors
  1. Teijiro Isokawa
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  2. Ferdinand Peper
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  3. Koji Ono
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  4. Nobuyuki Matsui
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Corresponding author

Correspondence to Teijiro Isokawa.

Additional information

A short version of the paper is 12th International conference on Cellular Automata for Research and Industry (ACRI2016), 2016 (Isokawa et al. 2016). This work was supported by a Grant-in-Aid for Scientific Research on Innovative Areas “Molecular Robotics” (No. 15H00825) of The Ministry of Education, Culture, Sports, Science, and Technology, Japan.

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Isokawa, T., Peper, F., Ono, K. et al. A universal Brownian cellular automaton with 3 states and 2 rules. Nat Comput 17, 499–509 (2018). https://doi.org/10.1007/s11047-017-9651-0

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  • DOI: https://doi.org/10.1007/s11047-017-9651-0

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