In polynomial and spline interpolation the k-th derivative of the interpolant, as a function of the mesh size h, typically converges at the rate of O(hd+1−k) as h → 0, where d is the degree of the polynomial or spline. In this paper we establish, in the important cases k = 1, 2, the same convergence rate for a recently proposed family of barycentric rational interpolants based on blending polyn...

ion Refinement with Craig Interpolation and Symbolic Pushdown Systems ? Javier Esparza, Stefan Kiefer, and Stefan Schwoon Institute for Formal Methods in Computer Science, University of Stuttgart {esparza,kiefersn,schwoosn}@informatik.uni-stuttgart.de Abstract. Counterexample-guided abstraction refinement (CEGAR) has proven to be a powerful method for software model-checking. In this paper, we ...

In this paper, we discourse an analysis of classical first-order predicate logic as a constraint satisfaction problem, CSP. First, will offer our general framework for CSPs, and then apply it to logic. We claim would function new semantics, Then, prove the soundness completeness theorems with respect semantics. The latter theorem, which be proven by proof-search method, implies cut-elimination ...

We describe new extensions of the Vampire theorem prover for computing tree interpolants. These extensions generalize Craig interpolation in Vampire, and can also be used to derive sequence interpolants. We evaluated our implementation on a large number of examples over the theory of linear integer arithmetic and integer-indexed arrays, with and without quantifiers. When compared to other metho...

A method is presented that connects the existence of uniform interpolants to the existence of certain sequent calculi. This method is applied to several modal logics and is shown to cover known results from the literature, such as the existence of uniform interpolants for the modal logic K. The results imply that for modal logics K4 and S4, which are known not to have uniform interpolation, cer...

In the study of approximation order, particularly in a multivariable setting, quasi-interpolants have played a major role. This report points out some limitations of quasi-interpolants and describes some recent results on approximation order obtained without the benefit of the quasi-interpolant idea. §1. Approximation Order In most general terms, “approximation order” is defined as follows. Def...

The potential beneets of a uniform version of interpolation are hindered by its absence from many expressive logics. This motivates a thorough investigation of appropriate expansions of known entailments so that an easy-to-derive, uniform presentation of the interpolants is supported. This paper presents the skeleton of a general construction and indicates that a potentially large class of enta...

Interpolation-based model checking (ITP) [14] is an efficient and complete model checking procedure. However, for large problems, interpolants generated by ITP might become extremely large, rendering the procedure slow or even intractable. In this work we present a novel technique for interpolant generation in the context of model checking. The main novelty of our work is that we generate small...