Logical formalisation and algorithms allow constructive, correct and complete solutions written in the language of production rules,

Boolean functions, together with their deductive proofs.

Time Complexities under Some Variations of

Boolean FunctionsIt helps in the realization of various

Boolean functions such as AND, OR, MUX, INVERTER, F1 and F2, as listed in Table 1.

He covers infeasible monotone systems of constraints; complexes, (hyper)graphs, and inequality systems; polytopes, positive bases, and inequality systems; monotone

Boolean functions, complexes, graphs, and inequality; and inequality systems, committees, (hyper)graphs, and alternative covers.

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.

[4] utilized near-bent

Boolean functions of five variables to generate 5x5 S-boxes to resist the differential attack; however, their algorithm was useful only to create an S-box of odd input bit number.

This approach is the generalization of BNs based on multilinear interpolation of

Boolean functions.

Boolean functions are replaced by their real-valued realizations called the Boolecubes or the Hillcubes.

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.

Let F be a class of

Boolean functions (implemented by a family of circuits C), and let [bar.F] = {[bar.F] | F [member of] F} be a class of the complement function [bar.F] of each function F and the class of the outsourced data set U' = {[psi] | [psi] [member of] U,'} and H be any one-way function.

Carlet (9) introduced a method called Welch and the multiplicative inverse functions that used in the S-boxes of the AES to deduce bounds on the second order nonlinearity for classes of cryptographic

Boolean functions. Mozaffari et al (10-17) used both S-box and inverse S-box and it was utilizing logic gates to malicious injected faults detection.

In its original version for

Boolean functions this term accounts for the output difference of pair of data points located at Hamming distance 2:

Same CGP approach was used by Miller [14] but again no testing instances were provided and his research was more aimed at comparing CGP to regular GA and Probabilistic Hillclimbers as a method to solve

Boolean functions.