This paper introduces a generalization of self-dual marked flattenings defined in the lattice of mappings. This definition provides a way to associate a self-dual operator to every mapping that decomposes an element into subelements (i.e. gives a cover). Contrary to classical flattenings whose definition relies on the complemented structure of the powerset lattices, our approach uses the pseudo...

Innnite behavior of nondeterministic nite state automata running over innnite trees or more generally over elements of an arbitrary algebraic structure is characterized by a calculus of xed point terms interpreted in powerset algebras. These terms involve the least and greatest xed point operators and disjunction as the only logical operation. A tight correspondence is established between a hie...

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

mobile robot navigation is one of the basic problems in robotics. in this paper, a new approachis proposed for autonomous mobile robot navigation in an unknown environment. the proposedapproach is based on learning virtual parallel paths that propel the mobile robot toward the trackusing a multi-layer, feed-forward neural network. for training, a human operator navigates themobile robot in some...

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...