Boolean and pseudo-Boolean functions play a central role in various areas of applied mathematics. We will focus here on their use in decision making, cooperative game theory, and engineering reliability theory. A discrete fuzzy measure on the finite set X = {1, . . . ,n} is a nondecreasing set function μ : 2 → [0,1] satisfying the boundary conditions μ(∅) = 0 and μ(X) = 1. For any subset S ⊆ X ...

Boolean functions used in cryptographic applications have to satisfy various cryptographic criteria. Although the choice of the criteria depends on the cryptosystem in which they are used, there are some properties (balancedness, nonlinearity, high algebraic degree, correlation immunity, propagation criteria) which a cryptographically strong Boolean function ought to have. We study the above me...

Algebraic immunity has been proposed as an important property of Boolean functions. To resist algebraic attack, a Boolean function should possess high algebraic immunity. It is well known now that the algebraic immunity of an n-variable Boolean function is upper bounded by ⌈ n 2 ⌉ . In this paper, for an odd integer n, we present a construction method which can efficiently generate a Boolean fu...

In this paper, a new algorithm based on Binary Decision Diagram (BDD) for the analysis of a system with multistate components is proposed. Each state of a multistate component is represented by a Boolean variable, and a multistate system is represented by a series of multistate fault trees. A Boolean algebra with restrictions on variables is used to address the dependence among these Boolean va...

Linear threshold functions (for real and Boolean inputs) have received much attention, for they are the component parts of many artificial neural networks. Linear threshold functions are exactly those functions such that the positive and negative examples are separated by a hyperplane. One extension of this notion is to allow separators to be surfaces whose equations are polynomials of at most ...