Concept Lattices Henry Soldano and Véronique Ventos 1 L.I.P.N, UMR-CNRS 7030, Université Paris-Nord, 93430 Villetaneuse, France 2 LRI, UMR-CNRS 8623, Université Paris-Sud, 91405 Orsay, France henry.soldano@lipn.univ-paris13.fr, ventos@lri.fr Abstract. We present a view of abstraction based on a structure preserving reduction of the Galois connection between a language L of terms and the powerse...

Coalgebra is an abstract framework for the uniform study of different kinds of dynamical systems. An endofunctor F determines both the type of systems (F-coalgebras) and a notion of behavioral equivalence (∼F) amongst them. Many types of transition systems and their equivalences can be captured by a functor F. For example, for deterministic automata the derived equivalence is language equivalen...

One of the continuing challenges in abstract interpretation is the creation of abstractions that yield analyses that are both tractable and precise enough to prove interesting properties about real-world programs. One source of difficulty is the need to handle programs with different behaviors along different execution paths. Disjunctive (powerset) abstractions capture such distinctions in a na...

In this paper we study the definition of generalized powerset of terms in the context of partially ordered monads. We provide a definition of the powerset of terms over acSLAT and study some possible directions for the definition of a partially ordered term monad.

The powerset construction is a standard method for converting a non-deterministic automaton into an equivalent deterministic one as far as language is concerned. In this short paper, we lift the powerset construction on automata to the more general framework of coalgebras with enriched state spaces. Examples of applications includes transducers, and Rabin probabilistic automata.

Abstract We prove that the existence of a measurable cardinal is equivalent to normal space whose modal logic coincides with Kripke frame isomorphic powerset two element set.

This paper introduces formative processes, composed by transitive partitions. Given a family F of sets, a formative process ending in the Venn partition of F is shown to exist. Sufficient criteria are also singled out for a transitive partition to model (via a function from set variables to unions of sets in the partition) all set-literals modeled by . On the basis of such criteria a procedure ...

We prove the decidability for a class of languages which extend BST and NP-completeness subclass them. The extended with unordered cartesian product, ordered product powerset fall in this last subclass.

Enumerating all solutions of a relational algebra equation is a natural and powerful operation which, when added as a query language primitive to the nested relational algebra, yields a query language for nested relational databases, equivalent to the well-known powerset algebra. We study sparse equations, which are equations with at most polynomially many solutions. We look at their complexity...