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Turing-Completeness of Asynchronous Non-camouflage Cellular Automata

  • Tatsuya YamashitaEmail author
  • Teijiro Isokawa
  • Ferdinand Peper
  • Ibuki Kawamata
  • Masami Hagiya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10248)

Abstract

Asynchronous Boolean totalistic cellular automata have recently attracted attention as promising models for the implementation of reaction-diffusion systems. It is unknown, however, to what extent they are able to conduct computation. In this paper, we introduce the so-called non-camouflage property, which means that a cell’s update is insensitive to neighboring states that equal its own state. This property is stronger than the Boolean totalistic property, which signifies the existence of states in a cell’s neighborhood, but is not concerned with how many cells are in those states. We argue that the non-camouflage property is extremely useful for the implementation of reaction-diffusion systems, and we construct an asynchronous cellular automaton with this property that is Turing-complete. This indicates the feasibility of computation by reaction-diffusion systems.

Keywords

Cellular Automaton Neighboring Cell Turing Machine Cell State Transition Rule 
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.

Notes

Acknowledgements

This work was supported by a Grant-in-Aid for Scientific Research on Innovative Areas “Molecular Robotics” (No. 15H00825 and No. 24104005) of The Ministry of Education, Culture, Sports, Science, and Technology, Japan.

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Copyright information

© IFIP International Federation for Information Processing 2017

Authors and Affiliations

  • Tatsuya Yamashita
    • 1
    Email author
  • Teijiro Isokawa
    • 2
  • Ferdinand Peper
    • 3
  • Ibuki Kawamata
    • 4
  • Masami Hagiya
    • 1
  1. 1.University of TokyoTokyoJapan
  2. 2.University of HyogoKobeJapan
  3. 3.NICT and Osaka UniversityOsakaJapan
  4. 4.Tohoku UniversitySendaiJapan

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