It is well known that free Boolean algebra on n generators isomorphic to the of functions variables. The distributive lattice monotone In this paper we introduce concept De Morgan function and prove Keywords: Antichain, function, algebra.

Any monotone Boolean function on a lattice can be described by the set of its minimal 1 values. If a lattice is given as a concept lattice, this set can be represented by the set of minimal hypotheses of a classification context. Enumeration of minimal hypotheses in output polynomial time is shown to be impossible unless P = NP, which shows that dualization of monotone functions on lattices wit...

For an odd integer n=2d?1, let B(n,d) be the subgraph of hypercube Qn induced by two largest layers. In this paper, we describe typical structure independent sets in and give precise asymptotics on number them. The proofs use Sapozhenko's graph container method a recently developed Jenssen Perkins, which combines lemma with cluster expansion for polymer models from statistical physics.

In this work we study the Boolean Networks of different geometric shape and lattice organization. It was revealed that no only a spatial shape but also type of lattice are very important for definition of the structure-dynamics relation. The regular structures do not give a critical regime in the investigated cases. Hierarchy together with the irregular structure reveals characteristic features...

A study is made of Boolean product representations of bounded lattices over the Stone space of their centres. Special emphasis is placed on relating topological properties such as clopen or regular open equalizers to their equivalent lattice theoretic counterparts. Results are also presented connecting various properties of a lattice with properties of its individual stalks. Mathematics Subject...

To any entailment relation Sco74] we associate a distributive lattice. We use this to give a construction of the product of lattices over an arbitrary index set, of the Vietoris construction, of the embedding of a distributive lattice in a boolean algebra, and to give a logical description of some spaces associated to mathematical structures.