相关论文: Formalizing IMO Problems and Solutions in Isabelle…
Physics provides fundamental laws that describe and predict the natural world. AI systems aspiring toward more general, real-world intelligence must therefore demonstrate strong physics problem-solving abilities: to formulate and apply…
Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…
We present an automated verification of the well-known modal logic cube in Isabelle/HOL, in which we prove the inclusion relations between the cube's logics using automated reasoning tools. Prior work addresses this problem but without…
The rapid advancement of large reasoning models has saturated existing math benchmarks, underscoring the urgent need for more challenging evaluation frameworks. To address this, we introduce OlymMATH, a rigorously curated, Olympiad-level…
Linear programming describes the problem of optimising a linear objective function over a set of constraints on its variables. In this paper we present a solver for linear programs implemented in the proof assistant Isabelle/HOL. This…
Using Isabelle/HOL, we verify a union-find data structure with an explain operation due to Nieuwenhuis and Oliveras. We devise a simpler, more naive version of the explain operation whose soundness and completeness is easy to verify. Then,…
Proprietary AI systems have recently demonstrated impressive capabilities on complex proof-based problems, with gold-level performance reported at the 2025 International Mathematical Olympiad (IMO). However, the training pipelines behind…
Economic growth, people's health, and urban development face challenges in the post-epidemic era. How to promote high-quality and sustainable urban development, improve citizens' sense of happiness, and solve problems in city management…
We present SMPLOlympics, a collection of physically simulated environments that allow humanoids to compete in a variety of Olympic sports. Sports simulation offers a rich and standardized testing ground for evaluating and improving the…
Mathematics olympiads are prestigious competitions, with problem proposing and solving highly honored. Building artificial intelligence that proposes and solves olympiads presents an unresolved challenge in automated theorem discovery and…
The ability of large language models to solve complex mathematical problems has progressed significantly, particularly for tasks requiring advanced reasoning. However, the scarcity of sufficiently challenging problems, particularly at the…
Most real-world optimization problems have multiple objectives. A system designer needs to find a policy that trades off these objectives to reach a desired operating point. This problem has been studied extensively in the setting of known…
The mathematical problems and their solutions of the Third International Students' Olympiad in Cryptography NSUCRYPTO'2016 are presented. We consider mathematical problems related to the construction of algebraic immune vectorial Boolean…
We formally introduce IsaVODEs (Isabelle verification with Ordinary Differential Equations), a framework for the verification of cyber-physical systems. We describe the semantic foundations of the framework's formalisation in the…
Formal verification of cyber-physical and robotic systems requires that we can accurately model physical quantities that exist in the real-world. The use of explicit units in such quantities can allow a higher degree of rigour, since we can…
The Orion-1 model by OpenAI is claimed to have more robust logical reasoning capabilities than previous large language models. However, some suggest the excellence might be partially due to the model "memorizing" solutions, resulting in…
The topics of Artificial intelligence (AI) and especially Machine Learning (ML) are increasingly making their way into educational curricula. To facilitate the access for students, a variety of platforms, visual tools, and digital games are…
During the last decade, Machine Learning (ML) has increasingly become a hot topic in the field of Computer Networks and is expected to be gradually adopted for a plethora of control, monitoring and management tasks in real-world…
Automated theorem provers are now commonly used within interactive theorem provers to discharge an increasingly large number of proof obligations. To maintain the trustworthiness of a proof, the automatically found proof must be verified…
This paper describes a formal theory of smooth vector fields, Lie groups and the Lie algebra of a Lie group in the theorem prover Isabelle. Lie groups are abstract structures that are composable, invertible and differentiable. They are…