Related papers: Generating Correctness Proofs with Neural Networks

We propose ProofNet++, a neuro-symbolic framework that enhances automated theorem proving by combining large language models (LLMs) with formal proof verification and self-correction mechanisms. Current LLM-based systems suffer from…

Generative Artificial Intelligence (GenAI) has demonstrated its capabilities in the present world that reduce human effort significantly. It utilizes deep learning techniques to create original and realistic content in terms of text,…

In recent months, large language models (LLMs) have made significant progress in mathematical proof generation, but further advancement is hindered by the lack of a large-scale, high-quality dataset of human-evaluated proofs. While…

Recent developments in deep neural networks (DNNs) have led to their adoption in safety-critical systems, which in turn has heightened the need for guaranteeing their safety. These safety properties of DNNs can be proven using tools…

A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…

Large language models (LLMs) have shown increasing competence in solving mathematical reasoning problems. However, many open-source LLMs still struggle with errors in calculation and semantic understanding during intermediate reasoning…

Fact verification systems typically rely on neural network classifiers for veracity prediction which lack explainability. This paper proposes ProoFVer, which uses a seq2seq model to generate natural logic-based inferences as proofs. These…

The automated generation of test code can reduce the time and effort required to build software while increasing its correctness and robustness. In this paper, we present RE-ASSERT, an approach for the automated generation of JUnit test…

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…

This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…

This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…

Visual Programming has recently emerged as an alternative to end-to-end black-box visual reasoning models. This type of method leverages Large Language Models (LLMs) to generate the source code for an executable computer program that solves…

Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…

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…

Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs…

Proof-oriented programming languages (POPLs) empower developers to write code alongside formal correctness proofs, providing formal guarantees that the code adheres to specified requirements. Despite their powerful capabilities, POPLs…

Despite the vast body of research literature proposing algorithms with formal guarantees, the amount of verifiable code in today's systems remains minimal. This discrepancy stems from the inherent difficulty of verifying code, particularly…

We develop the first (to the best of our knowledge) provably correct neural networks for a precise computational task, with the proof of correctness generated by an automated verification algorithm without any human input. Prior work on…

Formal verification offers a path to provably correct software, but writing verified code remains expensive enough that the technique is rarely used in production. Recent large language models can accelerate this work, and recent benchmarks…

Noisy data, non-convex objectives, model misspecification, and numerical instability can all cause undesired behaviors in machine learning systems. As a result, detecting actual implementation errors can be extremely difficult. We…