A Neurosymbolic Approach to Loop Invariant Generation via Weakest Precondition Reasoning

TL;DR

NeuroInv is a neurosymbolic method combining LLMs and symbolic reasoning to generate loop invariants, significantly improving success rates and scalability in automated program verification.

Contribution

This paper introduces NeuroInv, a novel neurosymbolic framework that integrates neural reasoning with symbolic verification to enhance loop invariant generation.

Findings

Achieves 99.5% success rate on Java program benchmarks.

Outperforms existing approaches in invariant generation accuracy.

Scales effectively to complex multi-loop programs.

Abstract

Loop invariant generation remains a critical bottleneck in automated program verification. Recent work has begun to explore the use of Large Language Models (LLMs) in this area, yet these approaches tend to lack a reliable and structured methodology, with little reference to existing program verification theory. This paper presents NeuroInv, a neurosymbolic approach to loop invariant generation. NeuroInv comprises two key modules: (1) a neural reasoning module that leverages LLMs and Hoare logic to derive and refine candidate invariants via backward-chaining weakest precondition reasoning, and (2) a verification-guided symbolic module that iteratively repairs invariants using counterexamples from OpenJML. We evaluate NeuroInv on a comprehensive benchmark of 150 Java programs, encompassing single and multiple (sequential) loops, multiple arrays, random branching, and noisy code segments. NeuroInv achieves a $99.5\%$ success rate, substantially outperforming the other evaluated approaches. Additionally, we introduce a hard benchmark of $10$ larger multi-loop programs (with an average of $7$ loops each); NeuroInv's performance in this setting demonstrates that it can scale to more complex verification scenarios.