Universal Totalistic Asynchonous Cellular Automaton and Its Possible Implementation by DNA

  • Teijiro IsokawaEmail author
  • Ferdinand Peper
  • Ibuki Kawamata
  • Nobuyuki Matsui
  • Satoshi Murata
  • Masami Hagiya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9726)


This paper presents a Cellular Automaton (CA) model designed for possible implementation by the reaction and diffusion of DNA strands. The proposed CA works asynchronously, whereby each cell undergoes its transitions independently from other cells and at random times. The state of a cell changes in a cyclic manner, rather than according to an any-to-any mapping. The transition rules are designed as totalistic, i.e., the next state of a cell is determined only by the number of states in the neighborhood of the cell, not by their relative positions. Universal circuit elements are designed for the CA as well as wires and crossings to connect them, which implies that the CA is Turing-complete.


Cellular Automata (CA) Transition Rules Circuit Elements Boolean Totalistic Input Wires 
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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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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Teijiro Isokawa
    • 1
    Email author
  • Ferdinand Peper
    • 2
  • Ibuki Kawamata
    • 3
  • Nobuyuki Matsui
    • 1
  • Satoshi Murata
    • 3
  • Masami Hagiya
    • 4
  1. 1.University of HyogoHimejiJapan
  2. 2.Center for Information and Neural Networks, National Institute of Information and Communications Technology, Osaka UniversityOsakaJapan
  3. 3.Tohoku UniversitySendaiJapan
  4. 4.The University of TokyoTokyoJapan

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