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Reversibility Of A Symmetric Linear Cellular Automata

Author

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  • A. MARTÍN DEL REY

    (Department of Applied Mathematics, E. P. S. de Ávila, Universidad de Salamanca, C/ Hornos Caleros 50, 05003-Ávila, Spain)

  • G. RODRÍGUEZ SÁNCHEZ

    (Department of Applied Mathematics, E. P. S. de Zamora, Universidad de Salamanca, Avda. Cardenal Cisneros 34, 49022-Zamora, Spain)

Abstract

The characterization of the size of the cellular space of a particular type of reversible symmetric linear cellular automata is introduced in this paper. Specifically, it is shown that those symmetric linear cellular with2k + 1cells, and whose transition matrix is ak-diagonal square band matrix with nonzero entries equal to 1 are reversible. Furthermore, in this case the inverse cellular automata are explicitly computed. Moreover, the reversibility condition is also studied for a general number of cells.

Suggested Citation

  • A. Martín Del Rey & G. Rodríguez Sánchez, 2009. "Reversibility Of A Symmetric Linear Cellular Automata," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1081-1086.
    • Handle: RePEc:wsi:ijmpcx:v:20:y:2009:i:07:n:s0129183109014217
    DOI: 10.1142/S0129183109014217
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    Cited by:

    1. A. Martín del Rey & R. Casado Vara & D. Hernández Serrano, 2019. "Reversibility of Symmetric Linear Cellular Automata with Radius r = 3," Mathematics, MDPI, vol. 7(9), pages 1-15, September.

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