The interest for information retrieval has existed long before the Internet. Boolean retrieval is the most simple of these retrieval methods and relies on the use of Boolean operators. The terms in a query are linked together with AND, OR and NOT. This method is often used in search engines on the Internet because it is fast and can therefore be used online. This method has also its problems. T...

Consider the Boolean model in IR, where the germs form a homogeneous Poisson point process with intensity λ and the grains are convex compact random sets. It is known (see e.g. Section 9.5.3 in Cressie (1993)) that Laslett’s rule transforms the exposed tangent points of the Boolean model into a homogeneous Poisson process with the same intensity λ. In the present paper, we give a simple proof o...

This paper deals with the representation of Boolean functions using artificial neural networks and points out three important results. First, using a polynomial as transfer function, a single neuron is able to represent a non-monotonous Boolean function. Second, the number of inputs in the neural network can be decreased if the binary values of the Boolean variables are encoded. This approach s...

Software model checking problems generally contain two different types of non-determinism: 1) non-deterministically chosen values; 2) the choice of interleaving among threads. Most modern software model checkers can handle only one source of non-determinism efficiently, but not both. This paper describes a SAT-based model checker for asynchronous Boolean programs that handles both sources effec...

We consider new complexity measures for the model of multilinear circuits with general multilinear gates introduced by Goldreich and Wigderson (ECCC, 2013). These complexity measures are related to the size of canonical constant-depth Boolean circuits, which extend the definition of canonical depth-three Boolean circuits. We obtain matching lower and upper bound on the size of canonical constan...

Gene interactions in cells can be represented by gene regulatory networks. A Boolean network models gene interactions according to rules where gene expression is represented by binary values (on / off or {1, 0}). In reality, however, the gene's state can have multiple values due to biological properties. Furthermore, the noisy nature of the experimental design results in uncertainty about a sta...

the aim of this paper is to extend results established by h. onoand t. kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. the main theorem states that a residuatedlattice a is directly indecomposable if and only if its boolean center b(a)is {0, 1}. we also prove that any linearly ordered residuated lattice and anylocal residuated lattice are d...