Interpolation is an important technique in computer aided verification and static analysis of programs. In particular, interpolants extracted from so-called local proofs are used in invariant generation and bounded model checking. An interpolant extracted from such a proof is a boolean combination of formulas occurring in the proof. In this talk we first describe a technique of generating and o...

1 Background and Introduction Let 27 and H be two inconsistent first order theories. Then by Craig's Interpolation Theorem, there is a sentence 8, called a Craig interpolant, such that 8 is t rue in 27 and false in H and every nonlogical symbol occurring in 8 occurs in bo th 27 and H. Craig interpolants can be used to solve the problem of learning a first order concept by letting 27 and H be th...

A finite element method of any order is applied on a Bakhvalov-type mesh to solve singularly perturbed convection--diffusion equation in 2D, whose solution exhibits exponential boundary layers. uniform convergence (almost) optimal proved by means carefully defined interpolant.

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...

In this paper, a new partition of unity ± the synchronized reproducing kernel (SRK) interpolant ± is derived. It is a class of meshless shape functions that exhibit synchronized convergence phenomenon: the convergence rate of the interpolation error of the higher order derivatives of the shape function can be tuned to be that of the shape function itself. This newly designed synchronized reprod...