Related papers: Understanding and Improving Automated Proof Synthe…
LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…
Recent advances in automated theorem proving leverages language models to explore expanded search spaces by step-by-step proof generation. However, such approaches are usually based on short-sighted heuristics (e.g., log probability or…
Synthesizing user-intended programs from a small number of input-output examples is a challenging problem with several important applications like spreadsheet manipulation, data wrangling and code refactoring. Existing synthesis systems…
In theorem proving, the task of selecting useful premises from a large library to unlock the proof of a given conjecture is crucially important. This presents a challenge for all theorem provers, especially the ones based on language…
Recent advancements in Generative AI and Large Language Models (LLMs) have enabled the creation of highly realistic synthetic content, raising concerns about the potential for malicious use, such as misinformation and manipulation.…
In this paper we demonstrate how logic programming systems and Automated first-order logic Theorem Provers (ATPs) can improve the accuracy of Large Language Models (LLMs) for logical reasoning tasks where the baseline performance is given…
Highly automated theorem provers like Dafny allow users to prove simple properties with little effort, making it easy to quickly sketch proofs. The drawback is that such provers leave users with little control about the proof search,…
Proof-oriented programs mix computational content with proofs of program correctness. However, the human effort involved in programming and proving is still substantial, despite the use of Satisfiability Modulo Theories (SMT) solvers to…
Recently, researchers have been working toward the development of practical general-purpose protocols for verifiable computation. These protocols enable a computationally weak verifier to offload computations to a powerful but untrusted…
Geometry theorem proving forms a major and challenging component in the K-12 mathematics curriculum. A particular difficult task is to add auxiliary constructions (i.e, additional lines or points) to aid proof discovery. Although there…
We show that interactive protocols between a prover and a verifier, a well-known tool of complexity theory, can be used in practice to certify the correctness of automated reasoning tools. Theoretically, interactive protocols exist for all…
Recent advancements in large language models (LLMs) have spurred growing interest in automatic theorem proving using Lean4, where effective tree search methods are crucial for navigating the underlying large proof search spaces. While the…
Static verification relying on an automated theorem prover can be very slow and brittle: since static verification is undecidable, correct code may not pass a particular static verifier. In this work we use metaprogramming to generate code…
Artificial Intelligence (AI) advancement is heavily dependent on access to large-scale, high-quality training data. However, in specialized domains such as healthcare, data acquisition faces significant constraints due to privacy…
Recent advancements, such as DeepSeek-Prover-V2-671B and Kimina-Prover-Preview-72B, demonstrate a prevailing trend in leveraging reinforcement learning (RL)-based large-scale training for automated theorem proving. Surprisingly, we discover…
Proving Unrealizability for Syntax-Guided Synthesis We consider the problem of automatically establishing that a given syntax-guided-synthesis (SyGuS) problem is unrealizable (i.e., has no solution). Existing techniques have quite limited…
The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…
Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean. However, we often want to optimize a formal proof with respect to various criteria, depending on its…
Generating code from natural-language requirements has become a primary route for LLM-assisted software development. Although LLMs can successfully complete small programming tasks, generating an entire complex project remains unreliable…
Mathematical reasoning remains a significant challenge for Large Language Models (LLMs) due to hallucinations. When combined with formal proof assistants like Lean, these hallucinations can be eliminated through rigorous verification,…