相关论文: Solving Hard Mizar Problems with Instantiation and…

We consider the problem of computing numerical invariants of programs by abstract interpretation. Our method eschews two traditional sources of imprecision: (i) the use of widening operators for enforcing convergence within a finite number…

The assignment problem is an essential problem in many application fields and frequently used to optimize resource usage. The problem is well understood and various efficient algorithms exist to solve the problem. However, it was unclear…

Mathematical reasoning would be one of the next frontiers for artificial intelligence to make significant progress. The ongoing surge to solve math word problems (MWPs) and hence achieve better mathematical reasoning ability would continue…

We present new integer linear programming (ILP) models for NP-hard optimisation problems in instances of the Stable Marriage problem with Ties and Incomplete lists (SMTI) and its many-to-one generalisation, the Hospitals / Residents problem…

We describe a very large improvement of existing hammer-style proof automation over large ITP libraries by combining learning and theorem proving. In particular, we have integrated state-of-the-art machine learners into the E automated…

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

We present a novel length-aware solving algorithm for the quantifier-free first-order theory over regex membership predicate and linear arithmetic over string length. We implement and evaluate this algorithm and related heuristics in the Z3…

Automated Theorem Proving (ATP) represents a core research direction in artificial intelligence for achieving formal reasoning and verification, playing a significant role in advancing machine intelligence. However, current large language…

We significantly improve the performance of the E automated theorem prover on the Isabelle Sledgehammer problems by combining learning and theorem proving in several ways. In particular, we develop targeted versions of the ENIGMA guidance…

Process supervision, using a trained verifier to evaluate the intermediate steps generated by a reasoner, has demonstrated significant improvements in multi-step problem solving. In this paper, to avoid the expensive effort of human…

This paper introduces and analyzes a preconditioned modified of the Hermitian and skew-Hermitian splitting (PMHSS). The large sparse continuous Sylvester equations are solved by PMHSS iterative algorithm based on nonHermitian, complex,…

Despite the advancements in large language models (LLMs) for mathematical reasoning, solving competition-level math problems remains a significant challenge, especially for open-source LLMs without external tools. We introduce the MMIQC…

It is known that the multiplication of an $N \times M$ matrix with an $M \times P$ matrix can be performed using fewer multiplications than what the naive $NMP$ approach suggests. The most famous instance of this is Strassen's algorithm for…

Strategy iteration is a technique frequently used for two-player games in order to determine the winner or compute payoffs, but to the best of our knowledge no general framework for strategy iteration has been considered. Inspired by…

We announce a tool for mapping derivations of the E theorem prover to Mizar proofs. Our mapping complements earlier work that generates problems for automated theorem provers from Mizar inference checking problems. We describe the tool,…

In model predictive control (MPC) an optimization problem has to be solved at each time step, which in real-time applications makes it important to solve these optimization problems efficiently and to have good upper bounds on worst-case…

Solving the Multi-Agent Path Finding (MAPF) problem optimally is known to be NP-Hard for both make-span and total arrival time minimization. While many algorithms have been developed to solve MAPF problems, there is no dominating optimal…

We introduce the first program synthesis engine implemented inside an SMT solver. We present an approach that extracts solution functions from unsatisfiability proofs of the negated form of synthesis conjectures. We also discuss novel…

This work presents a comparative study of new and existing optimization and diagonalization methods for solving time-independent partial differential equations (PDEs) using matrix product states (MPS) in the quantized tensor-train formalism…

Automated Machine Learning encompasses a set of meta-algorithms intended to design and apply machine learning techniques (e.g., model selection, hyperparameter tuning, model assessment, etc.). TPOT, a software for optimizing machine…