Related papers: Feasible Interpolation for QBF Resolution Calculi
Dependency quantified Boolean formulas (DQBF) is a logic admitting existential quantification over Boolean functions, which allows us to elegantly state synthesis problems in verification such as the search for invariants, programs, or…
We introduce a novel generalization of Counterexample-Guided Inductive Synthesis (CEGIS) and instantiate it to yield a novel, competitive algorithm for solving Quantified Boolean Formulas (QBF). Current QBF solvers based on…
Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For…
Craig interpolation has become a versatile algorithmic tool for improving software verification. Interpolants can, for instance, accelerate the convergence of fixpoint computations for infinite-state systems. They also help improve the…
Resolution is the rule of inference at the basis of most procedures for automated reasoning. In these procedures, the input formula is first translated into an equisatisfiable formula in conjunctive normal form (CNF) and then represented as…
We consider interpolation-based derivative-free optimization in settings where only some derivatives are available. Such situations arise naturally in scientific computing applications involving simulations, adjoint-enabled components,…
In this paper we propose an enhanced version of the residual sub-sampling method (RSM) in [9] for adaptive interpolation by radial basis functions (RBFs). More precisely, we introduce in the context of sub-sampling methods a maximum profile…
This paper investigates linear programming based branch-and-bound using general disjunctions, also known as stabbing planes, for solving integer programs. We derive the first sub-exponential lower bound (in the encoding length $L$ of the…
We present efficient methods to interpolate data with a quantum computer that complement uploading techniques and quantum post-processing. The quantum algorithms are supported by the efficient Quantum Fourier Transform (QFT) and classical…
We develop foundations for computing Craig interpolants and similar intermediates of two given formulas with first-order theorem provers that construct clausal tableaux. Provers that can be understood in this way include efficient…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
Quantifier elimination (QE) and Craig interpolation (CI) are central to various state-of-the-art automated approaches to hardware and software verification. They are rooted in the Boolean setting and are successful for, e.g., first-order…
QBFs (quantified boolean formulas), which are a superset of propositional formulas, provide a canonical representation for PSPACE problems. To overcome the inherent complexity of QBF, significant effort has been invested in developing QBF…
This article presents a technique for proving problems hard for classes of the polynomial hierarchy or for PSPACE. The rationale of this technique is that some problem restrictions are able to simulate existential or universal quantifiers.…
Due to the expected disparity in quantum vs. classical clock speeds, quantum advantage for branch and bound algorithms is more likely achievable in settings involving large search trees and low operator evaluation costs. Therefore, in this…
This paper presents a feasibility-enhanced control barrier function (FECBF) framework for multi-UAV collision avoidance. In dense multi-UAV scenarios, the feasibility of the CBF quadratic program (CBF-QP) can be compromised due to internal…
This work presents a new interpolation tool, namely, cubic $q$-spline. Our new analogue generalizes a well known classical cubic spline. This analogue, based on the Jackson $q$-derivative, replaces an interpolating piecewise cubic…
In this short review we first recall combinatorial or ($0-$dimensional) quantum field theory (QFT). We then give the main idea of a standard QFT method, called the intermediate field method, and we review how to apply this method to a…
This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish some new results, clarify the range of…
The growing availability of computational resources has significantly increased the interest of the scientific community in performing complex multi-physics and multi-domain simulations. However, the generation of appropriate computational…