Characterization Of any Non-linear Boolean function Using A Set of Linear Operators
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.
Cite
@article{arxiv.0808.1641,
title = {Characterization Of any Non-linear Boolean function Using A Set of Linear Operators},
author = {Sudhakar Sahoo and Pabitra Pal Choudhury and Mithun Chakraborty},
journal= {arXiv preprint arXiv:0808.1641},
year = {2008}
}
Comments
12 pages, 4 figures, 2 table. Submitted for possible publication in the International Journal of Computer Mathematics and Applications, July 2008