Related papers: Lean-auto: An Interface between Lean 4 and Automat…
We describe an experiment in large-scale autoformalization of algebraic topology in an Interactive Theorem Proving (ITP) environment, where the workload is distributed among multiple LLM-based coding agents. Rather than relying on static…
In our research, we introduce a new concept called "LLM Augmented Pentesting" demonstrated with a tool named "Pentest Copilot," that revolutionizes the field of ethical hacking by integrating Large Language Models (LLMs) into penetration…
Our study presents a new framework that incorporates the Analytic Hierarchy Process (AHP) and Generative Pre-trained Transformer 4 (GPT-4) large language model (LLM), bringing novel approaches to cybersecurity Multiple-criteria Decision…
Formal verification using interactive theorem provers ensures high-quality software. However, writing proof scripts for interactive theorem provers is labor-intensive and requires deep expertise. Recent studies have leveraged deep learning…
Enabling more concise and modular proofs is essential for advancing formal reasoning using interactive theorem provers (ITPs). Since many ITPs, such as Rocq and Lean, use tactic-style proofs, learning higher-level custom tactics is crucial…
This paper introduces Isabelle/HoTT, the first development of homotopy type theory in the Isabelle proof assistant. Building on earlier work by Paulson, I use Isabelle's existing logical framework infrastructure to implement essential…
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…
Motivated by the transfer of proofs between proof systems, and in particular from first order automated theorem provers (ATPs) to interactive theorem provers (ITPs), we specify an extension of the TPTP derivation text format to describe…
Automated testing is essential for evaluating and improving the reliability of Large Language Models (LLMs), yet the lack of automated oracles for verifying output correctness remains a key challenge. We present LLMORPH, an automated…
AI-assisted theorem proving can now generate substantial Lean developments for olympiad-level mathematics, but the evidential status of such developments depends on which declarations are actually verified. This paper reports a Lean 4…
We introduce a new theorem prover for classical higher-order logic named auto2. The prover is designed to make use of human-specified heuristics when searching for proofs. The core algorithm is a best-first search through the space of…
LLMs have demonstrated strong mathematical reasoning abilities by leveraging reinforcement learning with long chain-of-thought, yet they continue to struggle with theorem proving due to the lack of clear supervision signals when solely…
Automated Theorem Proving (ATP) in formal languages remains a formidable challenge in AI, demanding rigorous logical deduction and navigating vast search spaces. While large language models (LLMs) have shown promising performance, existing…
We describe a prototype theorem prover, UTP2, developed to match the style of hand-written proof work in the Unifying Theories of Programming semantical framework. This is based on alphabetised predicates in a 2nd-order logic, with a strong…
The remarkable capabilities and intricate nature of Artificial Intelligence (AI) have dramatically escalated the imperative for specialized AI accelerators. Nonetheless, designing these accelerators for various AI workloads remains both…
Large language models (LLMs) often struggle with mathematical problems that require exact computation or multi-step algebraic reasoning. Tool-integrated reasoning (TIR) offers a promising solution by leveraging external tools such as code…
Large Language Models (LLMs) have revolutionized the field of Natural Language Processing thanks to their ability to reuse knowledge acquired on massive text corpora on a wide variety of downstream tasks, with minimal (if any) tuning steps.…
Recent advances in Large Language Model (LLM) based Generative AI techniques have made it feasible to translate enterprise-level code from legacy languages such as COBOL to modern languages such as Java or Python. While the results of…
The demand for synthetic data in mathematical reasoning has increased due to its potential to enhance the mathematical capabilities of large language models (LLMs). However, ensuring the validity of intermediate reasoning steps remains a…
As artificial intelligence (AI) gains greater adoption in a wide variety of applications, it has immense potential to contribute to mathematical discovery, by guiding conjecture generation, constructing counterexamples, assisting in…