Ranking LLM-Generated Loop Invariants for Program Verification

Abstract

Synthesizing inductive loop invariants is fundamental to automating program verification. In this work we observe that Large Language Models (such as {gpt-3.5} or {gpt-4}) are capable of synthesizing loop invariants for a class of programs in a 0-shot setting, yet require several samples to generate the correct invariants. This can lead to a large number a calls to a program verifier to establish an invariant. To address this issue, we propose a {re-ranking} approach for the generated results of LLMs. We have designed a ranker that can distinguish between correct inductive invariants and incorrect attempts based on the problem definition. The ranker is optimized as a contrastive ranker. Experimental results demonstrate that this re-ranking mechanism significantly improves the ranking of correct invariants among the generated candidates, leading to a notable reduction in the number of calls to a verifier.