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...

‎in this paper we try to extend geometric concepts in the context of operator valued tensors‎. ‎to this end‎, ‎we aim to replace the field of scalars $ mathbb{r} $ by self-adjoint elements of a commutative $ c^star $-algebra‎, ‎and reach an appropriate generalization of geometrical concepts on manifolds‎. ‎first‎, ‎we put forward the concept of operator-valued tensors and extend semi-riemannian...

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 article, we provide a splitting method for solving monotone inclusions in real Hilbert space involving four operators: maximally monotone, monotone-Lipschitzian, cocoercive, and monotone-continuous operator. The proposed takes advantage of the intrinsic properties each operator, generalizing forward–backward–half-forward Tseng’s algorithm with line search. At iteration, our defines step...

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.