Bounded Model Checking (BMC) is one of the most paradigmatic practical applications of Boolean Satisfiability (SAT). The utilization of SAT in model checking has allowed significant performance gains and, as a consequence, a large number of commercial verification tools now include SAT-based model checkers. Recent work has provided SAT-based BMC with completeness conditions, and this is general...

We give a method of constructing an interpolant for linear equality, and inequality constraints over the rational numbers. Our method is based on efficient rewriting techniques, and does not require the use of combination methods. The interpolant is constructed in such a way that it reflects the structure of the rewrite proof.

The linear arithmetic solver in Yices was specifically designed for SMT provers, providing fast support for operations like adding and deleting constraints. We give a procedure for developing interpolants based on the results of the Yices arithmetic solver. For inequalities over real numbers, the interpolant is computed directly from the one contradictory equation and associated bounds. For int...

This paper presents a ray tracer that facilitates near-interactive scene editing with incremental rendering; the user can edit the scene both by manipulating objects and by changing the viewpoint. Our system uses object-space radiance interpolants to accelerate ray tracing by approximating radiance, while bounding error. We introduce a new hierarchical data structure, the ray segment tree (RST)...

This paper is an overview of recent developments in the construction of finite element interpolants, which are C-conforming on polygonal domains. In 1975, Wachspress proposed a general method for constructing finite element shape functions on convex polygons. Only recently has renewed interest in such interpolants surfaced in various disciplines including: geometric modeling, computer graphics,...

In this paper, we present a generalized entropy criterion for solving the rational Nevanlinna–Pick problem for + 1 interpolating conditions and the degree of interpolants bounded by . The primal problem of maximizing this entropy gain has a very well-behaved dual problem. This dual is a convex optimization problem in a finite-dimensional space and gives rise to an algorithm for finding all inte...

The use of interpolants in model checking is becoming an enabling technology to allow fast and robust verification of hardware and software. The application of encodings based on the theory of arrays, however, is limited by the impossibility of deriving quantifier-free interpolants in general. In this paper, we show that, with a minor extension to the theory of arrays, it is possible to obtain ...

We present a general and simple procedure to construct quasi-interpolants in hierarchical spaces, which are composed of a hierarchy of nested spaces. The hierarchical quasi-interpolants are described in terms of the truncated hierarchical basis. Once for each level in the hierarchy a quasi-interpolant is selected in the corresponding space, the hierarchical quasi-interpolants are obtained witho...

The use of Craig interpolants has enabled the development of powerful hardware and software model checking techniques. Efficient algorithms are known for computing interpolants in rational and real linear arithmetic. We focus on subsets of integer linear arithmetic. Our main results are polynomial time algorithms for obtaining proofs of unsatisfiability and interpolants for conjunctions of line...

We describe a compositional approach to Craig interpolation based on the heuristic that simpler proofs of special cases are more likely to generalize. The method produces simple interpolants because it is able to summarize a large set of cases using one relatively simple fact. In particular, we present a method for finding such simple facts in the theory of linear rational arithmetic. This make...