We propose a monotone multigrid method based on a B–spline basis of arbitrary smoothness for the efficient numerical solution of elliptic variational inequalities on closed convex sets. In order to maintain monotonicity (upper bound) and quasi–optimality (lower bound) of the coarse grid corrections, we propose coarse grid approximations of the obstacle function which are based on B–spline expan...

We propose a monotone multigrid method based on a B–spline basis of arbitrary smoothness for the efficient numerical solution of elliptic variational inequalities on closed convex sets. In order to maintain monotonicity (upper bound) and quasi–optimality (lower bound) of the coarse grid corrections, we propose coarse grid approximations of the obstacle function which are based on B–spline expan...

Propositional interpolation is widely used as a means of overapproximation to achieve efficient SAT-based symbolic model checking. Different verification applications exploit interpolants for different purposes; it is unlikely that a single interpolation procedure could provide interpolants fit for all cases. This paper describes the PeRIPLO framework, an interpolating SAT-solver that implement...

We discuss the construction of C 2 cubic spline quasi-interpolation schemes defined on a refined partition. These are reduced in terms degrees freedom compared to those existing literature. Namely, we provide rule for reducing them by imposing super-smoothing conditions while preserving full smoothness and precision. In addition, subdivision rules means blossoming. The derived designed express ...

Craig interpolation is a well known method of abstraction successfully used in both hardware and software model checking. The logical strength of interpolants can affect the quality of approximations and consequently the performance of the model checkers. Recently, it was observed that for the same resolution proof a complete lattice of interpolants ordered by strength can be derived. Most stat...

One of the main challenges in software verification is efficient and precise compositional analysis of programs with procedures and loops. Interpolation methods remains one of the most promising techniques for such verification, and are closely related to solving Horn clause constraints. We introduce a new notion of interpolation, disjunctive interpolation, which solves a more general class of ...