Component updates always bear the risk of negatively influencing the operativeness of software systems. Due to improper combinations of component versions, dependencies may break. In practise this often turns out to be due to missing or incompatible interfaces and signatures (syntactical interface) but may also be caused by changes in behavior or quality. In this paper we model the problem of f...

We frame feature selection as a representation problem within a wider task of clustering feature vectors, and root its solution on a special procedure for extracting from them a set of boolean components that we expect to be independent. The overall clustering procedure is based on a divide et impera strategy: first give data a suitable representation then compute an assignment function. With t...

In Boolean algebra, true statements are denoted 1 and false statements are denoted 0. A Boolean function acts on a set of these Boolean values and outputs a set of Boolean values (usually just one). The most common Boolean operators used are NOT, AND, OR, and XOR. 2.1 NOT NOT is a Boolean function that takes in one Boolean value and outputs its negation. Let x be a Boolean variable. NOT(x) is d...

The aim of this paper is to completely classify all aggregation functions based on the notion of arity gap. We first establish explicit descriptions of the arity gap of the Lovász extensions of pseudo-Boolean functions and, in particular, of the Choquet integrals. Then we consider the wider class of order-preserving functions between arbitrary, possibly different, posets, and show that similar ...

in this paper the concept of an $omega$- almost boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $omega$- almost boolean ring over a locally boolean space.

The minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f . In 1958, Markov determined the inversion complexity of every Boolean function and particularly proved that ⌈log 2 (n+ 1)⌉ NOT gates are sufficient to compute any Boolean function on n variables. In this paper, we consider circuits computing non-deterministically and dete...

Higher order differential cryptanalysis is based on the property of higher order derivatives of Boolean functions that the degree of a Boolean function can be reduced by at least 1 by taking a derivative on the function at any point. We define fast point as the point at which the degree can be reduced by at least 2. In this paper, we show that the fast points of a n-variable Boolean function fo...

Reasoning with Boolean Algebras is just propositional reasoning. This is well investigated and a lot of good algorithms have been developed. Other formal systems, for example mathematical programming for reasoning about arithmetical equation systems, are equally well developed. Combining such a system with a Boolean component where the Boolean expressions are interpreted as sets, would allow on...