Intrinsic universality of a 1-dimensional reversible Cellular Automaton

  • Jérôme Olivier Durand-Lose
Parallel and Distributed Systems II
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1200)


This paper deals with simulation and reversibility in the context of Cellular Automata (ca). We recall the definitions of ca and of the Block (bca) and Partitioned (pca) subclasses. We note that pca simulate ca. A simulation of reversible ca (r-ca) with reversible pca is built contradicting the intuition of known undecidability results. We build a 1-r-ca which is intrinsic universal, i.e., able to simulate any 1-r-ca.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Amoroso and Y. Patt. Decision procedure for surjectivity and injectivity of parallel maps for tessellation structure. Journal of Computer and System Sciences, 6:448–464, 1972.Google Scholar
  2. 2.
    C. H. Bennett. Logical reversibility of computation. IBM Journal of Research and Development, 6:525–532, 1973.Google Scholar
  3. 3.
    J. O. Durand-Lose. Reversible cellular automaton able to simulate any other reversible one using partitioning automata. In latin '95, number 911 in Lecture Notes in Computer Science, pages 230–244. Springer-Verlag, 1995.Google Scholar
  4. 4.
    J. O. Durand-Lose. Automates Cellulaires, Automates à Partitions et Tas de Sable. PhD thesis, labri, 1996. In French.Google Scholar
  5. 5.
    G. A. Hedlung. Endomorphism and automorphism of the shift dynamical system. Mathematical System Theory, 3:320–375, 1969.CrossRefGoogle Scholar
  6. 6.
    J. Kari. Reversibility of 2D cellular automata is undecidable. Physica D, 45:379–385, 1990.CrossRefGoogle Scholar
  7. 7.
    J. Kari. Reversibility and surjectivity problems of cellular automata. Journal of Computer and System Sciences, 48(1):149–182, 1994.CrossRefGoogle Scholar
  8. 8.
    J. Kari. Representation of reversible cellular automata with block permutations. Mathematical System Theory, 29:47–61, 1996.Google Scholar
  9. 9.
    N. Margolus. Physics-like models of computation. Physica D, 10:81–95, 1984.CrossRefMathSciNetGoogle Scholar
  10. 10.
    B. Martin. A universal cellular automaton in quasi-linear time and its S-n-m form. Theoretical Computer Science, 123:199–237, 1994.CrossRefGoogle Scholar
  11. 11.
    E. Moore. Machine models of self-reproduction. In Proceeding of Symposium on Applied Mathematics, volume 14, pages 17–33, 1962.Google Scholar
  12. 12.
    K. Morita. Computation-universality of one-dimensional one-way reversible cellular automata. Information Processing Letters, 42:325–329, 1992.CrossRefGoogle Scholar
  13. 13.
    K. Morita. Reversible simulation of one-dimensional irreversible cellular automata. Theoretical Computer Science, 148:157–163, 1995.CrossRefGoogle Scholar
  14. 14.
    J. Myhill. The converse of Moore's garden-of-eden theorem. In Proceedings of the Symposium of Applied Mathematics, number 14, pages 685–686, 1963.Google Scholar
  15. 15.
    D. Richardson. Tessellations with local transformations. Journal of Computer and System Sciences, 6:373–388, 1972.Google Scholar
  16. 16.
    T. Toffoli. Computation and construction universality of reversible cellular automata. Journal of Computer and System Sciences, 15:213–231, 1977.Google Scholar
  17. 17.
    T. Toffoli and N. Margolus. Cellular Automata Machine — A New Environment for Modeling. MIT press, Cambridge, MA, 1987.Google Scholar
  18. 18.
    T. Toffoli and N. Margolus. Invertible cellular automata: A review. Physica D, 45:229–253, 1990.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Jérôme Olivier Durand-Lose
    • 1
  1. 1.LaBRIUniversité Bordeaux ITalence CedexFrance

Personalised recommendations