Universal Totalistic Asynchonous Cellular Automaton and Its Possible Implementation by DNA

  • Teijiro Isokawa
  • 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)

Abstract

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.

References

  1. 1.
    Adachi, S., Lee, J., Peper, F., Umeo, H.: Kaleidoscope of life: a 24-neighbourhood outer-totalistic cellular automaton. Phys. D 237(6), 800–817 (2008)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Adleman, L.M.: Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 (1994)CrossRefGoogle Scholar
  3. 3.
    Biafore, M.: Cellular automata for nanometer-scale computation. Phys. D 70, 415–433 (1994)CrossRefMATHGoogle Scholar
  4. 4.
    Capcarrere, M.S., Sipper, M., Tomassini, M.: Two-state, \(r=1\) cellular automaton that classifies density. Phys. Rev. Lett. 77, 4969–4971 (1996)CrossRefGoogle Scholar
  5. 5.
    Hagiya, M., Wang, S., Kawamata, I., Murata, S., Isokawa, T., Peper, F., Imai, K.: On DNA-based gellular automata. In: Ibarra, O.H., Kari, L., Kopecki, S. (eds.) UCNC 2014. LNCS, vol. 8553, pp. 177–189. Springer, Heidelberg (2014)Google Scholar
  6. 6.
    Jonoska, N., Seeman, N.C.: Molecular ping-pong game of life on a two-dimensional dna origami array. Philos. Trans. R. Soc. Lond. A: Math. Phys. Eng. Sci. 373(2046) (2015). (Article Number 20140215)Google Scholar
  7. 7.
    Minsky, M.: Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)MATHGoogle Scholar
  8. 8.
    Montagne, K., Plasson, R., Sakai, Y., Fujii, T., Rondelez, Y.: Programming an in vitro DNA oscillator using a molecular networking strategy. Mol. Syst. Biol. 7(1), 476–485 (2011)CrossRefGoogle Scholar
  9. 9.
    Murata, S., Konagaya, A., Kobayashi, S., Hagiya, M.: Molecular robotics: a new paradigm for artifacts. New Gener. Comput. 31(1), 27–45 (2013)CrossRefGoogle Scholar
  10. 10.
    Padirac, A., Fujii, T., Rondelez, Y.: Bottom-up construction of in vitro switchable memories. Proc. Natl Acad. Sci. U.S.A. 109(47), E3212–E3220 (2012)CrossRefGoogle Scholar
  11. 11.
    Priese, L.: Automata and concurrency. Theor. Comput. Sci. 25(3), 221–265 (1983)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Rondelez, Y.: Competition for catalytic resources alters biological network dynamics. Phys. Rev. Lett. 108(1), 018102 (2012)CrossRefGoogle Scholar
  13. 13.
    Scalise, D., Schulman, R.: Emulating cellular automata in chemical reaction-diffusion networks. In: Murata, S., Kobayashi, S. (eds.) DNA 2014. LNCS, vol. 8727, pp. 67–83. Springer, Heidelberg (2014)Google Scholar
  14. 14.
    Toffoli, T.: CAM: a high-performance cellular-automaton machine. Phys. D 10, 195–204 (1984)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Teijiro Isokawa
    • 1
  • 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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