Definition 7 Nonlinearity: Let, f be a Boolean function of variables, [x.

Definition 10 Algebraic Normal Form: Any Boolean function can be expressed as xor of conjunctions and a Boolean constant, True or False.

For a fixed boolean function of k variables f let [A.

By a boolean function we mean a function f : [{0,1}.

Thus, a boolean circuit C will compute a boolean function f:{0,1}2?

Note that a family of boolean functions can be infinite whereas a basis is always finite.

Keywords: Random structures, Constraint satisfaction problems,

Boolean functions, Sensitivity, Satisfiability, Phase transition, Threshold.

NATO Advanced Study Institute on

Boolean Functions in Cryptology and Information Security (2007: Zvenigorod, Russia) Ed.

He provides essential mathematical background for discussing spectral methods, then delves into spectral logic and its applications, covering various transforms for multiple-valued functions, polynomial expressions and representations for switching and multiple-value functions, spectral analysis of

Boolean functions, and spectral synthesis and optimization of combinatorial and sequential devices.

The text presents an integrated treatment of the fundamental theory of logic functions and applications in the design of digital devices and systems, which is intended to allow students to see the similarities and differences between various theoretical approaches to the representation, manipulation, and optimization of

Boolean functions.

They cover general properties of correlation, applications of correlation to the communication of information, finite fields, feedback shift register sequences, randomness measurements and m- sequences, transforms of sequences and functions, cyclic difference sets and binary sequences with two-level autocorrelation, cyclic Hadamard sequences, correlation of

Boolean functions, and applications to radar, sonar, synchronization and CDMA wireless technology.

of California, San Diego) cover

Boolean functions and computer arithmetic, logic, number theory and cryptography, sets and functions, equivalence and order, and induction, sequences and series, all in discrete units with multiple choice questions for review.