Related papers: Interpolation-Based GR(1) Assumptions Refinement
In logics with the Craig interpolation property (CIP) the existence of an interpolant for an implication follows from the validity of the implication. In logics with the projective Beth definability property (PBDP), the existence of an…
Gravitational lens modeling of spatially resolved sources is a challenging inverse problem with many observational constraints and model parameters. We examine established pixel-based source reconstruction algorithms for de-lensing the…
Classical approximation and learning methods are typically optimized for interpolation over a sampled domain {\Omega}, with no guarantees on their behavior in an extrapolation region {\Xi}, where small in-domain errors may amplify. We…
A new effective solution to the problem of Hermite $G^1$ interpolation with a clothoid curve is here proposed, that is a clothoid that interpolates two given points in a plane with assigned unit tangent vectors. The interpolation problem is…
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…
Specifications for reactive systems often consist of environment assumptions and system guarantees. An implementation should not only be correct, but also robust in the sense that it behaves reasonably even when the assumptions are…
The aim of this paper is to derive a refined first-order expansion formula in Rn, the goal being to get an optimal reduced remainder, compared to the one obtained by usual Taylor's formula. For a given function, the formula we derived is…
Parametric model order reduction by matrix interpolation allows for efficient prediction of the behavior of dynamic systems without requiring knowledge about the underlying parametric dependency. Within this approach, reduced models are…
We construct approximate Fekete point sets for kernel-based interpolation by maximising the determinant of a kernel Gram matrix obtained via truncation of an orthonormal expansion of the kernel. Uniform error estimates are proved for kernel…
In this paper we present a novel method to overcome membrane locking of thin shells. An interpolation operator into the so-called Regge finite element space is inserted in the membrane energy term to weaken the implicitly given kernel…
Generalized Reactivity(1) (GR(1)) synthesis is a reactive synthesis approach in which the specification is split into two parts: a symbolic game graph, describing the safe transitions of a system, a liveness specification in a subset of…
This paper presents a general high-order kernel regularization technique applicable to all four integral operators of Calder\'on calculus associated with linear elliptic PDEs in two and three spatial dimensions. Like previous density…
With the commercial availability of mixed precision hardware, mixed precision GMRES-based iterative refinement schemes have emerged as popular approaches for solving sparse linear systems. Existing analyses of these approaches, however, are…
Structured Kernel Interpolation (SKI) (Wilson et al. 2015) helps scale Gaussian Processes (GPs) by approximating the kernel matrix via interpolation at inducing points, achieving linear computational complexity. However, it lacks rigorous…
We introduce skipping refinement, a new notion of correctness for reasoning about optimized reactive systems. Reasoning about reactive systems using refinement involves defining an abstract, high-level specification system and a concrete,…
In this paper we present a counter-example guided abstraction and approximation refinement (CEGAAR) technique for {\em partial predicate abstraction}, which combines predicate abstraction and fixpoint approximations for model checking…
In this chapter, we present six different proofs of Craig interpolation for the modal logic K, each using a different set of techniques (model-theoretic, proof-theoretic, syntactic, automata-theoretic, using quasi-models, and algebraic). We…
While the computation of Craig interpolants for description logics (DLs) with the Craig Interpolation Property (CIP) is well understood, very little is known about the computation and size of interpolants for DLs without CIP or if one aims…
Studies of hadron resonances and their properties are limited by the accuracy and consistency of measured datasets, which can originate from many different experiments. We have used Gaussian Processes (GP) to build interpolated datasets,…
In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the…