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Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…
Decentralized large language model (LLM) inference promises transparent and censorship resistant access to advanced AI, yet existing verification approaches struggle to scale to modern models. Proof of Quality (PoQ) replaces cryptographic…
Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as…
Ensuring that collections of natural-language facts are globally consistent is essential for tasks such as fact-checking, summarization, and knowledge base construction. While Large Language Models (LLMs) can assess the consistency of small…
Mathematics formalisation is the task of writing mathematics (i.e., definitions, theorem statements, proofs) in natural language, as found in books and papers, into a formal language that can then be checked for correctness by a program. It…
Quantum algorithms for computational linear algebra promise up to exponential speedups for applications such as simulation and regression, making them prime candidates for hardware realization. But these algorithms execute in a model that…
Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different tools are being increasingly used in…
Program verifiers such as Dafny automate proofs by outsourcing them to an SMT solver. This automation is not perfect, however, and the solver often requires hints in the form of assertions, creating a burden for the proof engineer. In this…
While the use of formal verification techniques is well established in the development of mission-critical software, it is still rare in the production of most other kinds of software. We share our experience that a formal verification tool…
The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO and have made significant progress. This paper focuses on formal verification,…
Foundational verification allows programmers to build software which has been empirically shown to have high levels of assurance in a variety of important domains. However, the cost of producing foundationally verified software remains…
Formally verifying system properties is one of the most effective ways of improving system quality, but its high manual effort requirements often render it prohibitively expensive. Tools that automate formal verification, by learning from…
We present $\textbf{Korean SimpleQA (KoSimpleQA)}$, a benchmark for evaluating factuality in large language models (LLMs) with a focus on Korean cultural knowledge. KoSimpleQA is designed to be challenging yet easy to grade, consisting of…
In mathematics, it is common practice to have several constructions for the same objects. Mathematicians will identify them modulo isomorphism and will not worry later on which construction they use, as theorems proved for one construction…
Large Language Models (LLMs) demonstrate impressive mathematical reasoning abilities, but their solutions frequently contain errors that cannot be automatically checked. Formal theorem proving systems such as Lean 4 offer automated…
Recently, with the chain of thought (CoT) prompting, large language models (LLMs), e.g., GPT-3, have shown strong reasoning ability in several natural language processing tasks such as arithmetic, commonsense, and logical reasoning.…
We describe a method for building composable and extensible verification procedures within the Coq proof assistant. Unlike traditional methods that rely on run-time generation and checking of proofs, we use verified-correct procedures with…
In order to increase user confidence, many automated theorem provers provide certificates that can be independently verified. In this paper, we report on our progress in developing a standalone tool for checking the correctness of…
Large language models (LLMs) demonstrate superior reasoning capabilities compared to small language models (SLMs), but incur substantially higher costs. We propose COllaborative REAsoner (COREA), a system that cascades an SLM with an LLM to…
We present CoqPilot, a VS Code extension designed to help automate writing of Coq proofs. The plugin collects the parts of proofs marked with the admit tactic in a Coq file, i.e., proof holes, and combines LLMs along with…