Related papers: An Instantiation-Based Approach for Solving Quanti…
In the article \The State of SAT", the authors asked whether a procedure dramatically different from DPLL can be found for handling unsatisfiable instances. This study proposes a new linear programming approach to address this issue…
Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories. In this survey, we explain the combination of propositional satisfiability and…
Let $\mathcal{L}_{\mathcal{X}}$ be the language of first-order, decidable theory $\mathcal{X}$. Consider the language, $\mathcal{L}_{\mathcal{RQ}}(\mathcal{X})$, that extends $\mathcal{L}_{\mathcal{X}}$ with formulas of the form $\forall x…
This paper proposes and tests the first-ever reduced basis warm-start iterative method for the parametrized linear systems, exemplified by those discretizing the parametric partial differential equations. Traditional iterative methods are…
We present a comprehensive study of chart visual question-answering(QA) task, to address the challenges faced in comprehending and extracting data from chart visualizations within documents. Despite efforts to tackle this problem using…
When solving combinatorial problems, pruning symmetric solution candidates from the search space is essential. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints…
Modern computationally-intensive applications often operate under time constraints, necessitating acceleration methods and distribution of computational workloads across multiple entities. However, the outcome is either achieved within the…
In this paper, we propose a framework based on the Retrospective Approximation (RA) paradigm to solve optimization problems with a stochastic objective function and general nonlinear deterministic constraints. This framework sequentially…
Building on advancements in Large Language Models (LLMs), we can tackle complex analytical and mathematical reasoning tasks requiring nuanced contextual understanding. A prime example of such complex tasks is modelling resource allocation…
Linear discriminant analysis (LDA) is a widely used technique for data classification. The method offers adequate performance in many classification problems, but it becomes inefficient when the data covariance matrix is ill-conditioned.…
Satisfiability Modulo the Theory of Nonlinear Real Arithmetic, SMT(NRA) for short, concerns the satisfiability of polynomial formulas, which are quantifier-free Boolean combinations of polynomial equations and inequalities with integer…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
In this paper, we present a quantum algorithm for approximating multivariate traces, i.e. the traces of matrix products. Our research is motivated by the extensive utility of multivariate traces in elucidating spectral characteristics of…
Solving a linear system $Ax=b$ is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are…
We discuss the topic of unsatisfiability proofs in SMT, particularly with reference to quantifier free non-linear real arithmetic. We outline how the methods here do not admit trivial proofs and how past formalisation attempts are not…
In this study, we propose the Quantum Gradient Flow Algorithm (QGFA), a novel quantum algorithm for solving symmetric positive definite (SPD) linear systems based on the variational formulation and time-evolution dynamics. Conventional…
Automatically generating high-quality step-by-step solutions to math word problems has many applications in education. Recently, combining large language models (LLMs) with external tools to perform complex reasoning and calculation has…
We propose an inference procedure for estimators defined by mathematical programming problems, focusing on the important special cases of linear programming (LP) and quadratic programming (QP). In these settings, the coefficients in both…
This paper addresses the problem of reliably and efficiently solving broad classes of long-horizon stochastic path planning problems. Starting with a vanilla RL formulation with a stochastic dynamics simulator and an occupancy matrix of the…