Related papers: On Boolean reliability algebra
Inspired by the fundamental results obtained by P. Halmos and A. Monteiro, concerning equivalence relations and monadic Boolean algebras, we recall the `concrete' Rauszer Boolean algebra pointed out by C. Rauszer (1971), via un preorder R.…
We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from…
A relation algebra is measurable if the identity element is a sum of atoms, and the square x;1;x of each subidentity atom x is a sum of non-zero functional elements. These functional elements form a group Gx. We prove that a measurable…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
The reliability of a system of components depends on reliability of each component. Thus, the initial statistical work should be the estimation of the reliability of each component of the system. This is not an easy task because when the…
We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification…
Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is called lineable whenever A contains, except for zero, an infinite dimensional vector subspace. If, additionally, X is endowed with richer…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
A measurable relation algebra is a relation algebra in which the identity element is a sum of atoms that can be measured in the sense that the "size" of each such atom can be defined in an intuitive and reasonable way (within the framework…
We present a novel method - LIBRE - to learn an interpretable classifier, which materializes as a set of Boolean rules. LIBRE uses an ensemble of bottom-up weak learners operating on a random subset of features, which allows for the…
Conditions for positive and polynomial recurrence have been proposed for a class of reliability models of two elements with transitions from working state to failure and back. As a consequence, uniqueness of stationary distribution of the…
Fuzzy optimization deals with the problem of determining 'optimal'solutions of an optimization problem when some of the elements that appear in the problem are not precise. In real situations it is usual to have information, in systems…
Although algebraic structures are frequently analyzed using unary and binary operations, they can also be effectively defined and unified through ternary operations. In this context, we introduce structures that contain two constants and a…
Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…
We prove that in a locally finite dimensional Lie algebra L, any maximal, locally solvable subalgebra (Borel subalgebra) is the stabilizer of a maximal, generalized flag in an integrable, faithful module over L.
We propound the thesis that there is a limitation to the number of possible structures which are axiomatically endowed with identities involving operations. In the case of algebras with a binary operation satisfying a formally reducible (to…
We compute the nonlinearity of Boolean functions with Groebner basis techniques, providing two algorithms: one over the binary field and the other over the rationals. We also estimate their complexity. Then we show how to improve our…
The author has recently introduced an abstract algebraic framework of analogical proportions within the general setting of universal algebra. This paper studies analogical proportions in the boolean domain consisting of two elements 0 and 1…
We describe several families of efficiently implementable Boolean functions achieving provable trade-offs between resiliency, nonlinearity, and algebraic immunity. In particular, the following statement holds for each of the function…