This paper presents a general theory of system composition for \possibilistic" security properties. We see that these properties fall outside of the AlpernSchneider safety/liveness domain and hence, are not subject to the Abadi-Lamport Composition Principle. We then introduce a set of trace constructors called selective interleaving functions and show that possibilistic security properties are ...

Violator Spaces were introduced by J. Matoušek et al. in 2008 as generalization of Linear Programming problems. Convex geometries were invented by Edelman and Jamison in 1985 as proper combinatorial abstractions of convexity. Convex geometries are defined by antiexchange closure operators. We investigate an interrelations between violator spaces and closure spaces and show that violator spaces ...

We deene the notion of meet-uniformity for closure operators on a complete lattice, which corresponds to co-additivity restricted to subsets mapped into the same element, and we study its properties. A class of closures given by principal lters and the downward closures are relevant examples of meet-uniform closures. Next, we introduce a lifting of a complete order by means of a meet-uniform cl...

In this paper we study the direct product decompositions of closure operations and lattices of closed sets. We characterize the direct product decompositions of lattices of closed sets in terms of closure operations, and nd those decompositions of lattices which correspond to the decompositions of closures. If a closure on a nite set is represented by its implication base (i.e. a binary relatio...

The closure test MCT (meet-in-the-middle closure test) was introduced to analyze the algebraic properties of cryptosystems [KaRiSh]. Since MCT needs a large amount of memory, it is hard to implement with an ordinary meet-in-the-middle method. As a feasible version of MCT, this paper presents a switching closure test S C T which based on a new memoryless meet-in-the-middle method. To achieve the...

We deal with the problem of combining sets of independence statements coming from different experts. It is known that the independence model induced by a strictly positive probability distribution has a graphoid structure, but the explicit computation of the closure (w.r.t. graphoid properties) of a set of independence statements is a computational hard problem. For this, we rely on a compact s...

We prove that the class of locally testable affine-invariant properties is closed under sums, intersections and “lifts”. The sum and intersection are two natural operations on linear spaces of functions, where the sum of two properties is simply their sum as a vector space. The “lift” is a less natural property that has been studied before. Previously such results were known for “single-orbit c...

This paper is a contribution to formal ontology study. We propose a new model of knowledge representation by combining ontologies and topology. In order to represent atypical entities in the ontologies, we introduce topological operators of interior, exterior, border and closure. These operators allow us to describe whether an entity, belonging to a class, is typical or not. We define a system ...