The evolution of SAT technology over the last decade has motivated its application in model checking, initially through the utilization of SAT in bounded model checking (BMC) and, more recently, in unbounded model checking (UMC). This paper addresses the utilization of interpolants in UMC and proposes two techniques for improving the original interpolant-based UMC algorithm. These techniques in...

Baskakov operators and their inverses can be expressed as linear differential operators on polynomials. Recurrence relations are given for the computation of these coefficients. They allow the construction of the associated Baskakov quasi-interpolants (abbr. QIs). Then asymptotic results are provided for the determination of the convergence orders of these new quasi-interpolants. Finally some r...

Recently, a new class of surface-divergence free radial basis function interpolants has been developed for surfaces in R3. In this paper, several approximation results for this class of interpolants will be derived in the case of the sphere, S2. In particular, Sobolev-type error estimates are obtained, as well as optimal stability estimates for the associated interpolation matrices. In addition...

We describe an incremental algorithm for computing interpolants for a pair φA, φB of formulas in propositional logic. In contrast with the common approaches, our method does not require a proof of unsatisfiability of φA ∧ φB , and can be realized using any SAT solver as a black box. We achieve this by combining model enumeration with the ability to easily generate interpolants in the special ca...

In this paper, we address the problem of curve and surface reconstruction from sets of points. We introduce regular interpolants which are polygonal approximations of planar curves and surfaces verifying a local sampling criterion. Properties of regular interpolants lead to new polygonal reconstruction methods from sets of organized and unorganized points. These methods do not need any paramete...

Interpolation and Schematic Reasoning are shown to underlie critical and somewhat complementary aspects of designing and (syntactically) manipulating speciication modules. In addition, the presence of a Uniform presentation of interpolants facilitates the speciication of modules. Also, the ability to encapsulate and manipulate Uniform Schemata may assist us in reasoning with (abstractions of) h...

Although EL is a popular logic used in large existing knowledge bases, to the best of our knowledge no procedure has yet been proposed that computes uniform EL interpolants of general EL terminologies. Up to now, also the bounds on the size of uniform EL interpolants remain unknown. In this paper, we propose an approach based on proof theory and the theory of formal tree languages to computing ...

Interpolation is an important component of recent methods for program verification. It provides a natural and effective means for computing separation between the sets of ‘good’ and ‘bad’ states. The existing algorithms for interpolant generation are proof-based: They require explicit construction of proofs, from which interpolants can be computed. Construction of such proofs is a difficult tas...

We show how interpolants can be viewed as classifiers in supervised machine learning and the advantages this view provides. First, we are able to use off-the-shelf classification techniques, in particular support vector machines, for computing interpolants. Second, since classification algorithms are predictive, the interpolants computed via classification have a good chance of being generalize...

This report discusses a mathematical software package DKLAG5 which consists of a suite of FORTRAN subroutines for the numerical solution of systems of functional di erential equations with state dependent delays. The package implements continuously imbedded Runge{ Kutta methods which are based on C polynomial interpolants. These interpolants are exploited by the software to handle the necessary...