Related papers: An Instantiation-Based Approach for Solving Quanti…
We propose, analyze, and test a proximal-gradient method for solving regularized optimization problems with general constraints. The method employs a decomposition strategy to compute trial steps and uses a merit function to determine step…
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…
We investigate quantifier alternation hierarchies in first-order logic on finite words. Levels in these hierarchies are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…
Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, either directly or by inferring the unknown action of the…
To reliably model real robot characteristics, interval linear systems of equations allow to describe families of problems that consider sets of values. This allows to easily account for typical complexities such as sets of joint states and…
Satisfiability Modulo Theories (SMT) solvers check the satisfiability of quantifier-free first-order logic formulas. We consider the theory of non-linear real arithmetic where the formulae are logical combinations of polynomial constraints.…
Quantum algorithms for solving the Quantum Linear System (QLS) problem are among the most investigated quantum algorithms of recent times, with potential applications including the solution of computationally intractable differential…
Satisfiability Modulo Theory (SMT) has recently emerged as a powerful tool for solving various automated reasoning problems across diverse domains. Unlike traditional satisfiability methods confined to Boolean variables, SMT can reason on…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
We describe a framework for solving a broad class of infinite-dimensional linear equations, consisting of almost banded operators, which can be used to resepresent linear ordinary differential equations with general boundary conditions. The…
A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$-matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known…
Data assimilation (DA) methods use priors arising from differential equations to robustly interpolate and extrapolate data. Popular techniques such as ensemble methods that handle high-dimensional, nonlinear PDE priors focus mostly on state…
For regularized optimization that minimizes the sum of a smooth term and a regularizer that promotes structured solutions, inexact proximal-Newton-type methods, or successive quadratic approximation (SQA) methods, are widely used for their…
We deal with interval parametric systems of linear equations and the goal is to solve such systems, which basically comes down to finding an enclosure for a parametric solution set. Obviously we want this enclosure to be as tight as…
For typical first-order logical theories, satisfying assignments have a straightforward finite representation that can directly serve as a certificate that a given assignment satisfies the given formula. For non-linear real arithmetic…
In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers,…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing…
Solving constraints involving inductive (aka recursive) definitions is challenging. State-of-the-art SMT/CHC solvers and first-order logic provers provide only limited support for solving such constraints, especially when they involve,…
We present a stable and convergent method for solving initial value problems based on the use of differentiation matrices obtained by Lagrange interpolation. This implicit multistep-like method is easy-to-use and performs pretty well in the…