Boolean constraints play an important role in various constraint logic programming languages. In this paper we consider pseudo-Boolean constraints, that is equations and inequalities between pseudo-Boolean functions. A pseudoBoolean function is an integer-valued function of Boolean variables and thus a generalization of a Boolean function. Pseudo-Boolean functions occur in many application area...

Some novel learning strategies based on set covering in Hamming geometrical space are presented and proved, which are related to the three-layer Boolean neural network (BNN) for implementing an arbitrary Boolean function with lowcomplexity. Each hidden neuron memorizes a set of learning patterns, then the output layer combines these hidden neurons for explicit output as a Boolean function. The ...

Single look-ahead unit resolution (SLUR) algorithm is a nondeterministic polynomial time algorithm which for a given input formula in a conjunctive normal form (CNF) either outputs its satisfying assignment or gives up. A CNF formula belongs to the SLUR class if no sequence of nondeterministic choices causes the SLUR algorithm to give up on it. The SLUR class is reasonably large. It is known to...

In this paper a useful educational tool is presented for minimizing low order Boolean expressions. The algorithm follows the Karnaugh map looping approach. For the implementation, which provides optimal results, C++ coding was used on the Embedded Visual C++ 3.0 Pocket PC using Windows CE Operating System environment. In order to make the overall implementation efficient, the object oriented ap...

This paper presents an extension of the Maiorana-McFarland method for building Boolean functions with good cryptographic properties. The original Maiorana-McFarland construction was proposed to design bent functions. Then, it was extended in [1] to build highly nonlinear resilient functions. The classical construction splits the set of variables into two separate subsets. There, is proposed a d...

We establish a framework to integrate propositional logic with first-order logic. This is done in such a way that it optionally appears either as first-order logic over a Boolean algebra or as propositional logic including Boolean quantification. We describe and prove complexity bounds for extended quantifier elimination by virtual substitution for our theory. This extended quantifier eliminati...

Valued constraint satisfaction problems (VCSPs) are discrete optimisation problems with a Q-valued objective function given as a sum of fixed-arity functions, where Q = Q ∪ {∞} is the set of extended rationals. In Boolean surjective VCSPs variables take on labels from D = {0, 1} and an optimal assignment is required to use both labels from D. A classic example is the global mincut problem in gr...

The notion of the maximal number of mind changes for a Boolean function was defined and applied in several contexts. An application in complexity theory is the result of Wagner and Wechsung that the classes of the Boolean closure of NP are exactly the classes of the Boolean hierarchy over NP. The aim of this paper is to study the complexity of determining the maximal number of mind changes of a...

We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2n possible linear Boolean functions of n variables; given a linear Boolean function, the Bernstein-Vazirani quantum algorithm can deterministically identify which one of these Boolean functions we are given using just one single function query. The same...

This paper presents a new type of neuron, called Boolean neuron. We suggest algorithms for decomposition of Boolean functions sets based on Boolean neural networks that include only Boolean neurons. The advantages of these neural networks consist in the reduction of memory space and computation time in comparison to the representation of Boolean functions by usual neural networks. The Boolean n...