We study rough approximations based on indiscernibility relations which are not necessarily reflexive, symmetric or transitive. For this, we define in a lattice-theoretical setting two maps which mimic the rough approximation operators and note that this setting is suitable also for other operators based on binary relations. Properties of the ordered sets of the upper and the lower approximatio...

A topology ^"i is said to cover another topology T3 if ^Ç^i and no other topology may be included between the two. In this paper, we characterize the relationship between a Tj-topology and its covers. This characterization is used to prove that the lattice of 7\-topologies is both upper and lower semimodular. We also prove that the sublattice generated by the covers of a 7\-topology is isomorph...

The boolean hierarchy of partitions was introduced and studied by K. Wagner and S. Kosub, mostly over the lattice of NP -sets. We consider this hierarchy for the case of lattices having the reduction property and show that in this case the hierarchy behaves much easier and admits a deeper investigation. We completely characterize the hierarchy over some concrete important lattices, e.g. over th...

In this paper, we characterize self-dual elements of a free distributive lattice with n generators by means of a median operation on this lattice. Hence, we obtain a constructive characterization of Sperner's families, for which H is equal to Tr H. We construct some infinite sequences of these families. These results generalize those of N. M. Rivi6re (J. Combinatorial Theory 5 (1968), 229-234) ...

The performance of higher-order masked implementations lattice-based based key encapsulation mechanisms (KEM) is currently limited by the costly conversions between arithmetic and Boolean masking. While bitslicing has been shown to strongly speed up symmetric primitives, its use in arithmetic-to-Boolean Boolean-to-arithmetic masking conversion gadgets never thoroughly investigated. In this pape...

The problem of reconstructing the and-or expression of a monotone Boolean function starting from a fixed subset of its truth table is solved by adopting a proper algorithm, called Shadow Clustering (SC). It generates a collection of prime implicants by descending the portion of the diagram of the Boolean lattice (associated with the input domain) that lies beneath the available examples. Three ...

Lattice games are real-valued functions de...ned on a ...nite lattice L. The basic players are the nonzero join-irreducible elements of the lattice and the coalitions are its elements. If L is the Boolean algebra 2 then we obtain a n-person game. Gilboa and Lehrer introduced the global games, which are lattice games where L = ¦n, the lattice of all partitions of N ordered by re...nement. Faigle...

We use a boolean cellular automaton model to describe the diffusion limited dynamics of the irreversible reaction A+A → A+ S on a 1D lattice. We derive a set of equations for the dynamics of the empty interval probabilities from which explicit expressions for the particle concentration and the two point correlation can be obtained. It is shown that the long time dynamics is in agreement with th...

In this paper, first we will find the solution of the system A ∗ X ≤ b, where A, b are the known suitable matrices and X is the unknown matrix over a pseudoBoolean lattice. Then its application to find the solution of some fuzzy linear systems as well as finding the solution of the optimization problem Z = max{C∗X|A∗ X ≤ b} is discussed. Key-words: pseudo-Boolean lattice, linear programming, fu...

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.