Can LLM Aid in Solving Constraints with Inductive Definitions?
arXiv:2603.03668v1 Announce Type: cross 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 2
arXiv:2603.03668v1 Announce Type: cross 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.
Executive Summary
This study explores the potential of Large Language Models (LLMs) in solving constraints involving inductive definitions. The authors develop a novel neuro-symbolic approach that synergistically integrates LLMs with constraint solvers. The LLM generates auxiliary lemmas and conjectures, while the solver checks their validity and usefulness. Experimental results demonstrate a significant improvement in solving proof tasks involving inductive definitions, outperforming state-of-the-art SMT and CHC solvers. The study contributes to the advancement of AI-assisted proof verification and constraint solving. Its findings have implications for the development of more efficient and effective automated reasoning systems.
Key Points
- ▸ The study proposes a neuro-symbolic approach for solving constraints involving inductive definitions.
- ▸ The approach leverages LLMs to generate auxiliary lemmas and conjectures.
- ▸ Experimental results show a significant improvement in solving proof tasks involving inductive definitions.
Merits
Strength of LLMs in Generating Auxiliary Lemmas
The study demonstrates the efficacy of LLMs in generating necessary auxiliary lemmas for reasoning about inductive definitions, which is a challenging task for state-of-the-art SMT/CHC solvers and first-order logic provers.
Improvement over State-of-the-Art Solvers
The study shows that the proposed approach can improve the state-of-the-art SMT and CHC solvers, solving considerably more proof tasks involving inductive definitions, around 25% more.
Demerits
Limited Generalizability
The study's findings may not generalize to all types of constraints and inductive definitions, as the experimental results were based on a specific benchmark suite comprising algebraic data types and recurrence relations.
Dependence on High-Quality LLMs
The effectiveness of the proposed approach relies on the quality of the LLMs used, which may limit its applicability in real-world scenarios where high-quality LLMs may not be readily available.
Expert Commentary
The study's proposed approach represents a significant advancement in the field of AI-assisted proof verification and constraint solving. The results demonstrate the efficacy of LLMs in generating necessary auxiliary lemmas and conjectures, which is a challenging task for state-of-the-art SMT/CHC solvers and first-order logic provers. However, the study's findings are not without limitations, as the experimental results were based on a specific benchmark suite, and the effectiveness of the proposed approach relies on the quality of the LLMs used. Nevertheless, the study's results have significant implications for the development of more efficient and effective automated reasoning systems, particularly in the context of proof verification and constraint solving.
Recommendations
- ✓ Future studies should investigate the generalizability of the proposed approach to a wider range of constraints and inductive definitions.
- ✓ Researchers should explore the development of high-quality LLMs that can be used in real-world scenarios, which is critical for the effective deployment of the proposed approach.
