In this paper a Boolean minimization algorithm is considered and implemented as an applet in Java. The application is based on the Quine-McCluskey simplification technique with some modifications. The given application can be accessed on line since it is posted on the World Wide Web (WWW), with up to four variables, at the URL http://www.csam.montclair.edu/∼antoniou/bs. After extensive testing,...

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...

Linear threshold functions (for real and Boolean inputs) have received much attention, for they are the component parts of many artiicial 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 a...

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 ...

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...

Recently there has been great interest in the design and study of evolvable systems in order to control the behavior of physically embedded systems. Due to the complexity of their architecture and their interaction with the environment, a Model-based Autonomous System approach was proposed by Williams to integrate a priori knowledge and reasoning methods of di erent kinds (Williams & Nayak 1996...

Given a bijective vectorial Boolean function Z~-1-Z~, define the correlation matrix P as an N x N matrix, N = 2 n-1, whose entries are given as the squares of the correlation coefficients between nonzero linear combinations of the component Boolean functions of F and nonzero linear Boolean functions of the same n variables. Let A denote the number of nonzero entries in P. When F is chosen unifo...

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...