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The challenge of formal proof generation has a rich history, but with modern techniques, we may finally be at the stage of making actual progress in real-life mathematical problems. This paper explores the integration of ChatGPT and basic…
Education in the practical applications of logic and proving such as the formal specification and verification of computer programs is substantially hampered by the fact that most time and effort that is invested in proving is actually…
Large language models (LLMs) have shown promise in proving formal theorems using proof assistants such as Lean. However, existing methods are difficult to reproduce or build on, due to private code, data, and large compute requirements.…
The requirements engineering (RE) phase is pivotal in developing high-quality software. Integrating advanced modelling techniques with large language models (LLMs) and formal verification in a logical style can significantly enhance this…
We introduce ProofGrid, a benchmark suite for evaluating LLM reasoning through machine-checkable proofs rather than final answers alone. ProofGrid contains 15 tasks spanning proof writing, proof checking, proof masking, and proof…
Program refinement involves correctness-preserving transformations from formal high-level specification statements into executable programs. Traditional verification tool support for program refinement is highly interactive and lacks…
Automatically generating formal specifications including loop invariants, preconditions, and postconditions for legacy code is critical for program understanding, reuse and verification. However, the inherent complexity of control and data…
Recent advances in automated theorem proving (ATP) through LLMs have highlighted the potential of formal reasoning with Lean 4 codes. However, ATP has not yet be revolutionized by the recent posttraining scaling as demonstrated by Open AI…
Reasoning is essential for closed-domain QA systems in which procedural correctness and policy compliance are critical. While large language models (LLMs) have shown strong performance on many reasoning tasks, recent work reveals that their…
Large language models (LLMs) are increasingly used to generate requirements specifications, design documents, code, and test cases. In contrast, much less attention has been given to a more difficult assurance problem: statically verifying…
Autoformalization, the process of translating informal statements into formal logic, has gained renewed interest with the emergence of powerful Large Language Models (LLMs). While LLMs show promise in generating structured outputs from…
We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for interactive theorem proving and discovery with LLMs. Human…
We study the classical problem of verifying programs with respect to formal specifications given in the linear temporal logic (LTL). We first present novel sound and complete witnesses for LTL verification over imperative programs. Our…
This thesis documents a voyage towards truth and beauty via formal verification of theorems. To this end, we develop libraries in Lean 4 that present definitions and results from diverse areas of MathematiCS (i.e., Mathematics and Computer…
Large language models (LLMs) have demonstrated significant potential in formal theorem proving, yet state-of-the-art performance often necessitates prohibitive test-time compute via massive roll-outs or extended context windows. In this…
The molecular computing has been successfully employed to solve more and more complex computation problems. However, as an important complex problem, the model checking are still far from fully resolved under the circumstance of molecular…
How to apply automated verification technology such as model checking and static program analysis to millions of lines of embedded C/C++ code? How to package this technology in a way that it can be used by software developers and engineers,…
Using AI to write formal proofs for mathematical problems is a challenging task that has seen some advancements in recent years. Automated systems such as Lean can verify the correctness of proofs written in formal language, yet writing the…
Large Language Models (LLMs) show promise in automated software engineering, yet their guarantee of correctness is frequently undermined by erroneous or hallucinated code. To enforce model honesty, formal verification requires LLMs to…
Evaluating statement autoformalization, translating natural language mathematics into formal languages like Lean 4, remains a significant challenge, with few metrics, datasets, and standards to robustly measure progress. In this work, we…