Related papers: SMT and Functional Equation Solving over the Reals…
The progress of Large Language Models (LLMs) like ChatGPT raises the question of how they can be integrated into education. One hope is that they can support mathematics learning, including word-problem solving. Since LLMs can handle…
Optimal symbol detection for multiple-input multiple-output (MIMO) systems is known to be an NP-hard problem. Conventional heuristic algorithms are either too complex to be practical or suffer from poor performance. Recently, several…
Standardized math assessments require expensive human pilot studies to establish the difficulty of test items. We investigate the predictive value of open-source large language models (LLMs) for evaluating the difficulty of multiple-choice…
Although demonstrating remarkable performance on reasoning tasks, Large Language Models (LLMs) still tend to fabricate unreliable responses when confronted with problems that are unsolvable or beyond their capability, severely undermining…
This paper considers the state estimation problem for nonlinear dynamic systems with unknown but bounded noises. Set membership filter (SMF) is a popular algorithm to solve this problem. In the set membership setting, we investigate the…
We consider a multidimensional extremal problem formulated in terms of tropical mathematics. The problem is to minimize a nonlinear objective function, which is defined on a finite-dimensional semimodule over an idempotent semifield,…
The problem of finding small unsatisfiable cores for SAT formulas has recently received a lot of interest, mostly for its applications in formal verification. However, propositional logic is often not expressive enough for representing many…
Computing properties of molecular systems rely on estimating expectations of the (unnormalized) Boltzmann distribution. Molecular dynamics (MD) is a broadly adopted technique to approximate such quantities. However, stable simulations rely…
This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum…
In problem solving, understanding the problem that one seeks to solve is an essential initial step. In this paper, we propose computational methods for facilitating problem understanding through the task of recognizing the unknown in…
Mathematical optimization is ubiquitous in modern applications. However, in practice, we often need to use nonlinear optimization models, for which the existing optimization tools such as Cplex or Gurobi may not be directly applicable and…
In this paper, we describe our winning approach to solving the Lane Following Challenge at the AI Driving Olympics Competition through imitation learning on a mixed set of simulation and real-world data. AI Driving Olympics is a two-stage…
Robust optimization(RO) is an important tool for handling optimization problem with uncertainty. The main objective of RO is to solve optimization problems due to uncertainty associated with constraints satisfying all realizations of…
Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results concerning discrepancy principle…
Submodular function minimization (SFM) is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint…
We show, contrary to the optimism about LLM's problem-solving abilities, fueled by the recent gold medals that were attained, that a problem exists -- Yu Tsumura's 554th problem -- that a) is within the scope of an IMO problem in terms of…
Large language models (LLMs) have achieved strong performance on reasoning benchmarks, yet their ability to solve real-world problems requiring end-to-end workflows remains unclear. Mathematical modeling competitions provide a stringent…
Test-time scaling has enabled Large Language Models (LLMs) with remarkable reasoning capabilities, particularly in mathematical domains, through intermediate chain-of-thought (CoT) reasoning before generating final answers. However, the…
In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point…
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…