boolean operation

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.

Adams and Tavares pointed out that if the linear sum of the Boolean function [f.sub.i] of each component of the designed nxn S-box was [2.sup.n-1], f was then abijection [44].

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].

Generally speaking, Boolean dynamic modeling of regulatory network follows three steps: (1) reconstructing the network; (2) identifying Boolean functions from the network topological structure; (3) analyzing the dynamics of the system with or without node perturbations.

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.