Characterization Of any Non-linear Boolean function Using A Set of Linear Operators

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Global dynamics of a non-linear Cellular Automata is, in general irregular, asymmetric and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable. In the past efforts have been made to systematize non-linear CA evolutions in the light of Boolean derivatives and Jacobian Matrices. In this paper two different efforts have been made: first we try to systematize non-linear CA evolution in the light of deviant states and non-deviant states. For all the non-deviant states the nearest linear rule matrix is applicable where as for the deviant states we have a set of other matrices. Second using algebraic manipulation, an efficient algorithm is proposed by which every Non-linear Boolean function can be characterized by a sequence of binary matrices.
12 pages, 4 figures, 2 table. Submitted for possible publication in the International Journal of Computer Mathematics and Applications, July 2008

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Computational Complexity, Cellular Automata and Lattice Gases

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http://salesiana.dossiersoluciones.com/handle/123456789/166899

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0808.1641
 http://arxiv.org/abs/0808.1641

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arXiv