Related papers: Munkres' General Topology Autoformalized in Isabel…
The Isabelle Archive of Formal Proofs has grown to a significant size in the past years. It makes up for an impressive body of research, which enables a number of statistical approaches to various aspects in theorem proving, and has not yet…
Formal methods is pivotal for verifying the reliability of critical systems through rigorous mathematical proofs. However, its adoption is hindered by labor-intensive manual proofs and the expertise required to use theorem provers. Recent…
We present a comprehensive, in-depth review of ideation assisted by large language models (LLMs), highlighting emerging trends and identifying unaddressed research gaps. In total, we examined 61 studies investigating the application of LLMs…
Isabelle/HOL augments classical higher-order logic with ad-hoc overloading of constant definitions---that is, one constant may have several definitions for non-overlapping types. In this paper, we present a mechanised proof that HOL with…
We extend a semantic verification framework for hybrid systems with the Isabelle/HOL proof assistant by an algebraic model for hybrid program stores, a shallow expression model for hybrid programs and their correctness specifications, and…
We show that for an arbitrary totally complex number field $L$ the (regularized) critical $L$-values of algebraic Hecke characters of $L$ divided by certain periods are algebraic integers. This relies on a new construction of an equivariant…
We propose a practical inexact augmented Lagrangian method (iALM) for nonconvex problems with nonlinear constraints. We characterize the total computational complexity of our method subject to a verifiable geometric condition, which is…
Turn-level metrics are widely used to evaluate properties of multi-turn human-LLM conversations, from safety and sycophancy to dialogue quality. However, consecutive turns within a conversation are not statistically independent -- a fact…
Combinatorial design theory studies set systems with certain balance and symmetry properties and has applications to computer science and elsewhere. This paper presents a modular approach to formalising designs for the first time using…
High-definition map transformations are essential in autonomous driving systems, enabling interoperability across tools. Ensuring their semantic correctness is challenging, since existing rule-based frameworks rely on manually written…
Language models for molecular design have scaled to hundreds of millions of parameters, yet how they learn chemical grammar is poorly understood. We train SMolLM, a 53K-parameter weight-shared transformer, to generate novel SMILES with 95%…
Language models (LMs) can perform complex reasoning either end-to-end, with hidden latent state, or compositionally, with transparent intermediate state. Composition offers benefits for interpretability and safety, but may need workflow…
Large language models (LLMs) are advanced artificial intelligence (AI) systems that can perform a variety of tasks commonly found in human intelligence tests, such as defining words, performing calculations, and engaging in verbal…
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…
Large language models (LLMs) exhibit failure modes on seemingly trivial tasks. We propose a formalisation of LLM interaction using a deterministic multi-tape Turing machine, where each tape represents a distinct component: input characters,…
We introduce a novel framework for evaluating the alignment between natural language plans and their expected behavior by converting them into Kripke structures and Linear Temporal Logic (LTL) using Large Language Models (LLMs) and…
A rigorous formalization of desired system requirements is indispensable when performing any verification task. This often limits the application of verification techniques, as writing formal specifications is an error-prone and…
We introduce HAMLET, a holistic and automated framework for evaluating the long-context comprehension of large language models (LLMs). HAMLET structures source texts into a three-level key-fact hierarchy at root-, branch-, and leaf-levels,…
On the one hand, ordered completion is a fundamental technique in equational theorem proving that is employed by automated tools. On the other hand, their complexity makes such tools inherently error prone. As a remedy to this situation we…
Formal verification via interactive theorem proving is increasingly used to ensure the correctness of critical systems, yet constructing large proof scripts remains highly manual and limits scalability. Advances in large language models…