An n x n S-box is defined by a vector
Boolean function [S.sub.n] : GF([2.sup.n]) [right arrow] GF([2.sup.n]), defined as
As discussed earlier, for n inputs there are 2 exp([2.sup.n]) possible
Boolean functions. These
Boolean functions can be mapped upon a limited set of NPN-equivalent classes.
where [x.sub.i](t + 1) [member of] {0,1} and [mathematical expression not reproducible] are the state and the
Boolean function of node [mathematical expression not reproducible] are the states of node [x.sub.i] predecessors in the previous time step, and is the number of predecessors of the node [x.sub.i].
For any proper binary
boolean function o, the complexity of [L.sub.m](a, b, -, d)o[L.sub.n](b, a, -, d) is maximal.
In its original version for
Boolean functions this term accounts for the output difference of pair of data points located at Hamming distance 2:
The truth table of
Boolean function of rule 24 is shown in Table 1.
CRA denotes the cost related attributes; the
Boolean function g is the correlation function of resources.
In the Boolean models, each gene's activity is expressed with ON or OFF, and each gene's state is described by the
Boolean function of other related genes' states.
As described by (1), the target [y.sub.i] at time t + 1 is completely determined by the values of its regulators at time t by means of a
Boolean function [f.sub.i] [member of] F, where F is a collection of
Boolean functions.
We observe that, by using these annotations, any data request ([C.sub.i] [member of] C) from BIGD can be written as a
Boolean function of keywords like:
Definition 4 Affine Function: A
Boolean function which can be expressed as 'xor' ([direct sum]) of some or all of its input variables and a Boolean constant is an affine function.
Graph-based algorithms for
Boolean function manipulation.
The combination of these is considered as universal because any general
Boolean function can be implemented with the combination of these logic primitives.
