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

Sudhakar Sahoo; Pabitra Pal Choudhury; Mithun Chakraborty

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arXiv · 0808.1641

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

Sudhakar Sahoo·Pabitra Pal Choudhury·Mithun Chakraborty

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Abstract

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.

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Sudhakar Sahoo, Pabitra Pal Choudhury, Mithun Chakraborty. 2008-08-12. Characterization Of any Non-linear Boolean function Using A Set of Linear Operators. https://arxiv.org/abs/0808.1641

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