Implementation of Arbitrary Boolean Functions via CNN

As a paradigm for nonlinear spatial-temporal processing, cellular nonlinear networks (CNN) are biologically inspired systems where computation emerges from a collection of simple locally coupled nonlinear cells. Our investigation is an exploration of implementing arbitrary Boolean functions by using CNN. A class of basic key Boolean functions is the class of linearly separable ones, which is identical to the class of uncoupled CNN with binary inputs and binary outputs. In our recent studies, we not only construct a neat binary input-output truth table and some interesting properties of the offset levels of uncoupled CNN, but also develop a practical design formula for the uncoupled CNN template. Especially, we obtain a criterion for LSBF (abbreviation of linearly separable Boolean function), which depends only on symbolic relations between a Boolean function´s outputs. Furthermore, we show that any linearly non-separable Boolean function can be decomposed as a logic operation of a series of linearly separable ones and can be implemented on CNN-UM