For any set-endofunctor T : Set→ Set there exists a largest subcartesian transformation μ to the filter functor F : Set → Set. Thus we can associate with every T -coalgebra A a certain filter-coalgebra AF. Precisely, when T weakly preserves preimages, μ is natural, and when T weakly preserves intersections, μ factors through the covariant powerset functor P, thus providing for every T -coalgebr...

In this paper we discuss Alpha Galois lattices (Alpha lattices for short) and the corresponding association rules. An alpha lattice is coarser than the related concept lattice and so contains fewer nodes, so fewer closed patterns, and a smaller basis of association rules. Coarseness depends on a a priori classification, i.e. a cover C of the powerset of the instance set I, and on a granularity ...

Formulation for calculating forward propagation and reflection in a 3D elastic structure based on the complex-screen method is given in this paper. The calculation of reflections is formulated based on the local Born approximation. When using a small angle approximation, the backscattering operator reduces to a screen operator which is similar to the forward screen propagator. Combining the for...

Kleisli simulation is a categorical notion introduced by Hasuo to verify finite trace inclusion. They allow us to give definitions of forward and backward simulation for various types of systems. A generic categorical theory behind Kleisli simulation has been developed and it guarantees the soundness of those simulations wrt. finite trace semantics. Moreover, those simulations can be aided by f...

Counterexample-based Refinement for Powerset Domains R. Manevich, J. Field , T. A. Henzinger, G. Ramalingam, and M. Sagiv 1 Tel Aviv University, {rumster,msagiv}@tau.ac.il 2 IBM T.J. Watson Research Center, [email protected] 3 EPFL, [email protected] 4 Microsoft Research India, [email protected] Abstract. Counterexample-guided abstraction refinement (CEGAR) is a powerful technique to scale auto...

Kripke semantics plays a fundamental role for modal logics where it often provides modular semantics allowing a clear treatment of various logics related by the addition of axioms or connectives. Kripke semantics is also the “natural semantics” for classical modal logic in the sense that it is given by the representation theory for modal algebras. The algebraic structure corresponding to a trad...

A set A of positive integers is called a coprime Diophantine powerset if the shifted product ab + 1 of two different elements a and b of A is always a pure power, and the occuring pure powers are all coprime. We prove that each coprime Diophantine powerset A ⊂ {1, . . . , N} has |A| ≤ 8000 logN/ log logN for sufficiently large N . The proof combines results from extremal graph theory with numbe...

In this paper, we study the nonexpansive properties of a generalized forward–backward splitting (G-FBS) operator, particularly under setting degenerate metric, from which follow convergence results in terms metric associated fixed-point iterations. The descent lemma and sufficient decrease property are also extended to case. It is further shown that G-FBS operator provides simplifying unifying ...

Paredaens and Van Gucht proved that the at relational algebra has the same expressive power as the nested relational algebra, as far as queries over at relations and with at results are concerned. We provide a new, very direct proof of this fact using a simulation technique. Our technique is also applied to partially answer a question posed by Suciu and Paredaens regarding the complexity of eva...