We present the PowerSetViewer visualization system for the lattice-based mining of powersets. Searching for items within the powerset of a universe occurs in many large dataset knowledge discovery contexts. Using a spatial layout based on a powerset provides a unified visual framework at three different levels: data mining on the filtered dataset, browsing the entire dataset, and comparing mult...

The nested relational algebra is often inadequate as a tool to handle nested relations, since several important queries, such as transitive closure, cannot expressed by it. On the other hand, the powerset algebra does allow the expression of transitive closure, but in a too expensive way. Therefore, we consider various other extensions to the nested algebra, such as least tixpoint and programmi...

We study the orbits under natural action of a permutation group G≤Sn on powerset

An algorithm for the uniform random generation of the powerset construction is presented. Given a combinatorial class I, together with a counting procedure and an unranking procedure (or simply a random generation procedure) for I, this algorithm provides counting and unranking (or random generation) procedures for P = powerset(I). For most combi-natorial structures, each random powerset of siz...

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 [email protected], [email protected] 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.