Can LLM Aid in Solving Constraints with Inductive Definitions?

TL;DR

This paper introduces a neuro-symbolic method that uses structured prompts to leverage LLMs for generating auxiliary lemmas, enhancing the ability of constraint solvers to handle inductive definitions in proof tasks.

Contribution

It presents a novel neuro-symbolic approach combining LLMs with constraint solvers to improve solving inductive constraints, which are difficult for traditional methods.

Findings

Improves proof task success rate by around 25%.

Enhances SMT/CHC solvers with LLM-generated lemmas.

Demonstrates effectiveness on diverse inductive constraint benchmarks.

Abstract

Solving constraints involving inductive (aka recursive) definitions is challenging. State-of-the-art SMT/CHC solvers and first-order logic provers provide only limited support for solving such constraints, especially when they involve, e.g., abstract data types. In this work, we leverage structured prompts to elicit Large Language Models (LLMs) to generate auxiliary lemmas that are necessary for reasoning about these inductive definitions. We further propose a neuro-symbolic approach, which synergistically integrates LLMs with constraint solvers: the LLM iteratively generates conjectures, while the solver checks their validity and usefulness for proving the goal. We evaluate our approach on a diverse benchmark suite comprising constraints originating from algebrai data types and recurrence relations. The experimental results show that our approach can improve the state-of-the-art SMT and CHC solvers, solving considerably more (around 25%) proof tasks involving inductive definitions, demonstrating its efficacy.