We present an approach to the classification of error messages in the context of static checking in the style of ESC/Java. The idea is to compute a semantics-based signature for each error message and then group together error messages with the same signature. The approach aims at exploiting modern verification techniques based on, e.g., Craig interpolation in order to generate small but signif...

We describe a model checker for infinite-state sequential programs, based on Craig interpolation and the lazy abstraction paradigm. On device driver benchmarks, we observe a speedup of up to two orders of magnitude relative to a similar tool using predicate abstraction.

In this paper, the expression of Weierstrass operators as differential operators on polynomials is used for the construction of associated quasi-interpolants. Then the convergence properties of these operators are studied. AMS Classification: 41A35.

We present a novel interpolation algorithm for effectively propositional logic (epr), a decidable fragment of first-order logic that enjoys a small-model property. epr is a powerful fragment of quantified formulas that has been used to model and verify a range of programs, including heap-manipulating programs and distributed protocols. Our interpolation technique samples finite models from two ...

In this paper, quadratic rules for obtaining approximate solution of definite integrals as well as single and double integrals using spline quasi-interpolants will be illustrated. The method is applied to a few test examples to illustrate the accuracy and the implementation of the method.

This paper considers the problem of assumptions refinement in the context of unrealizable specifications for reactive systems. We propose a new counterstrategy-guided synthesis approach for GR(1) specifications based on Craig’s interpolants. Our interpolation-based method identifies causes for unrealizability and computes assumptions that directly target unrealizable cores, without the need for...

The purpose of this paper is the investigation of strong converse results for Bernstein-Durrmeyer operators and their quasi-interpolants. For lower dimensions we improve known results by Knoop and Zhou [16] and Chen, Ditzian and Ivanov [5] in regard to the constants in their estimates and prove a strong converse theorem of type B for the quasi-interpolants introduced by Berdysheva, Jetter and S...

This paper presents new univariate linear non-uniform interpolatory subdivision constructions that yield high smoothness, C and C, and are based on least-degree spline interpolants. This approach is motivated by evidence, partly presented here, that constructions based on high-degree local interpolants fail to yield satisfactory shape, especially for sparse, non-uniform samples. While this impr...

In former articles we have given a formula for the error committed when interpolating a several times differentiable function by the sinc interpolant on a fixed finite interval. In the present workwe demonstrate the relevance of the formula through several applications: correction of the interpolant through the insertion of derivatives to increase its order of convergence, improvement of the ba...

A spectral collocation method based on rational interpolants and adaptive grid points is presented. The rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed Chebyshev points. The locations of the grid points are adapted to singularities of the underlying solution, and the locations of these singularities are appro...