Juan Carlos Seck Tuoh Mora
Spectral properties of reversible one-dimensional cellular automata
Mora, Juan Carlos Seck Tuoh; Vergara, Sergio V.Chapa; Mart�nez, Genaro Ju�rez; McIntosh, Harold V.
Authors
Sergio V.Chapa Vergara
Genaro Ju�rez Mart�nez
Harold V. McIntosh
Abstract
Reversible cellular automata are invertible dynamical systems characterized by discreteness, determinism and local interaction. This article studies the local behavior of reversible one-dimensional cellular automata by means of the spectral properties of their connectivity matrices. We use the transformation of every one-dimensional cellular automaton to another of neighborhood size 2 to generalize the results exposed in this paper. In particular we prove that the connectivity matrices have a single positive eigenvalue equal to 1; based on this result we also prove the idempotent behavior of these matrices. The significance of this property lies in the implementation of a matrix technique for detecting whether a one-dimensional cellular automaton is reversible or not. In particular, we present a procedure using the eigenvectors of these matrices to find the inverse rule of a given reversible one-dimensional cellular automaton. Finally illustrative examples are provided.
Citation
Martínez, G. J., Vergara, S. V., Mora, J. C. S. T., & McIntosh, H. V. (2003). Spectral properties of reversible one-dimensional cellular automata. International Journal of Modern Physics C, 14(3), 379-395. https://doi.org/10.1142/S0129183103004541
Journal Article Type | Article |
---|---|
Publication Date | Mar 1, 2003 |
Deposit Date | Jun 4, 2010 |
Publicly Available Date | Nov 16, 2016 |
Journal | International Journal of Modern Physics C |
Print ISSN | 0129-1831 |
Publisher | World Scientific Publishing |
Peer Reviewed | Peer Reviewed |
Volume | 14 |
Issue | 3 |
Pages | 379-395 |
DOI | https://doi.org/10.1142/S0129183103004541 |
Keywords | cellular automata, spectrum of graphs, idempotent behavior |
Public URL | https://uwe-repository.worktribe.com/output/1074037 |
Publisher URL | http://dx.doi.org/10.1142/S0129183103004541 |
Additional Information | Additional Information : Electronic version of an article published as International Journal of Bifurcation and Chaos, Vol. 14, issue 3, 2003, pp. 379-395 DOI: 10.1142/S0129183103004541 © World Scientific Publishing Company http://www.worldscinet.com/ijmpc/14/1403/S0129183103004541.html |
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