In this paper we analyse some fundamental interconnections between modularisation, (uniform) interpolants and information hiding and we explain how some compatible aspects of these concepts are combined in a notation independent method to establish the existence of a conservative extension J:Espec!Edev of a front-end speciication formalism Espec to a back-end formalism Edev so that Edev accommo...

The use of interpolants in model checking is progressively gaining importance. The application of encodings based on the theory of arrays, however, is limited by the impossibility of deriving quantifierfree interpolants in general. To overcome this problem, we have recently proposed a quantifier-free interpolation solver for a natural variant of the theory of arrays. However, arrays are usually...

Craig interpolation is successfully used in both hardware and software model checking. An important class of state-of-the-art interpolation algorithms is based on recursive procedures that generate interpolants from refutations of unsatisfiable conjunctions of formulas. We analyze this type of algorithms and develop a theoretical framework, called a parametric interpolation framework, for arbit...

We present a combination method for generating interpolants for a class of first-order theories. Using interpolant-generation procedures for individual theories as black-boxes, our method modularly generates interpolants for the combined theory. Our combination method applies for a broad class of first-order theories, which we characterize as equalityinterpolating Nelson-Oppen theories. This cl...

Interpolation by translates of \radial" basis functions is optimal in the sense that it minimizes the pointwise error functional among all comparable quasi{interpolants on a certain \native" space of functions F . Since these spaces are rather small for cases where is smooth, we study the behavior of interpolants on larger spaces of the form F 0 for less smooth functions 0. It turns out that in...

We show that Lagrange interpolants at the Chebyshev zeros yield best relative polynomial approximations of ð1þ ðaxÞÞ 1 on 1⁄2 1; 1 ; and more generally of Z N