Spectral properties of reversible one-dimensional cellular automata

Mora, J. C., Vergara, S. V., Martinez, G. J. and McIntosh, H. V. (2003) Spectral properties of reversible one-dimensional cellular automata. International Journal of Modern Physics C, 14 (3). pp. 379-395. ISSN 0129-1831

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Publisher's URL: http://dx.doi.org/10.1142/S0129183103004541

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 from 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 main result of this paper: the idempotent behavior of these matrices. This property is an important feature for detecting which one-dimensional cellular automata are reversible. Hence we present a procedure using the eigenvectors of these matrices to find the inverse rule for a given reversible one-dimensional cellular automaton. Finally illustrative examples are provided.

Item Type:Article
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
Uncontrolled Keywords:cellular automata, spectrum of graphs, idempotent behavior
Faculty/Department:Faculty of Environment and Technology
ID Code:7898
Deposited By: A. Lawson
Deposited On:04 Jun 2010 08:31
Last Modified:29 May 2014 19:12

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