Craig interpolation in SMT is difficult because, e. g., theory combination and integer cuts introduce mixed literals, i. e., literals containing local symbols from both input formulae. In this paper, we present a scheme to compute Craig interpolants in the presence of mixed literals. Contrary to existing approaches, this scheme neither limits the inferences done by the SMT solver, nor does it t...

In this paper, I discuss a method for increasing the continuity between two polynomial patches by adjusting their control points. The method described in this paper leaves the control points unchanged if the patches already meet with the desired level of continuity. Next I give two C degree n polynomial interpolation schemes that reproduce degree n polynomials, and show how to apply my continui...

Interpolating provers have a variety of applications in verification, including invariant generation and abstraction refinement. Here, we extended these methods to produce universally quantified interpolants and invariants, allowing the verification of programs manipulating arrays and heap data structures. We show how a paramodulation-based saturation prover, such as SPASS, can be modified in a...

A new class of differential operators on the simplex is introduced, which define weighted Sobolev norms andwhose eigenfunctions are orthogonal polynomialswith respect to Jacobiweights. These operators appear naturally in the study of quasi-interpolants which are intermediate between Bernstein– Durrmeyer operators and orthogonal projections on polynomial subspaces. The quasi-interpolants satisfy...

In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite dimensional linear case, and then find the optimum compact support function that best approximates a given filter in the least square sense (l2 norm). The be...

We derive a geometric criterion for the convexity of Powell-Sabin interpolants and present a multivariate generalization.