Related papers: Interpolation Properties and SAT-based Model Check…

The Craig interpolation property (CIP) states that an interpolant for an implication exists iff it is valid. The projective Beth definability property (PBDP) states that an explicit definition exists iff a formula stating implicit…

Recent research has established complexity results for the problem of deciding the existence of interpolants in logics lacking the Craig Interpolation Property (CIP). The proof techniques developed so far are non-constructive, and no…

This work investigates theoretically the interplay between interpolation and aggregation in regression. We establish that the $\gamma$-graph dimension characterizes learnability for a broad class of natural aggregation procedures.…

We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path…

It is often difficult to correctly implement a Boolean controller for a complex system, especially when concurrency is involved. Yet, it may be easy to formally specify a controller. For instance, for a pipelined processor it suffices to…

We show how variations of range-restriction and also the Horn property can be passed from inputs to outputs of Craig interpolation in first-order logic. The proof system is clausal tableaux, which stems from first-order ATP. Our results are…

Model checking has found a role in the engineering of reactive systems. However, model checkers are still strongly limited by the size of the system description they can check. Here we present a technique in which a system is simplified…

Abstraction, counterexample-guided refinement, and interpolation are techniques that are essential to the success of predicate-based program analysis. These techniques have not yet been applied together to explicit-value program analysis.…

We propose trace abstraction modulo probability, a proof technique for verifying high-probability accuracy guarantees of probabilistic programs. Our proofs overapproximate the set of program traces using failure automata, finite-state…

We present a simple method based on the stability and duality of the properties of sampling and interpolation, which allows one to substantially simplify the proofs of some classical results.

Abstraction (in its various forms) is a powerful established technique in model-checking; still, when unbounded data-structures are concerned, it cannot always cope with divergence phenomena in a satisfactory way. Acceleration is an…

We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…

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…

Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…

We show a projective Beth definability theorem for logic programs under the stable model semantics: For given programs $P$ and $Q$ and vocabulary $V$ (set of predicates) the existence of a program $R$ in $V$ such that $P \cup R$ and $P \cup…

Precisely modeling complex systems like cyber-physical systems is challenging, which often render model-based system verification techniques like model checking infeasible. To overcome this challenge, we propose a method called LAR to…

Spline interpolation is a widely used class of methods for solving interpolation problems by constructing smooth interpolants that minimize a regularized energy functional involving the Laplacian operator. While many existing approaches…

We prove a generalization of Maehara's lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig's interpolation property. As a…

Common model selection criteria, such as $AIC$ and its variants, are based on in-sample prediction error estimators. However, in many applications involving predicting at interpolation and extrapolation points, in-sample error cannot be…

A logic has uniform interpolation if its formulas can be projected down to given subsignatures, preserving all logical consequences that do not mention the removed symbols; the weaker property of (Craig) interpolation allows the projected…