Automated Strategy Invention for Confluence of Term Rewrite Systems

2024-11-10

arXiv.org

AI Summary

Automated confluence checking for term rewriting systems (TRSs) remains challenging due to the difficulty of automatically verifying confluence and the limitations of manually designed proof strategies. Method: This paper introduces the first machine learning–driven framework for automatic proof strategy invention. It pioneers the integration of reinforcement learning with symbolic reasoning, incorporating the CSI solver to autonomously explore and optimize within the strategy space. Additionally, it constructs the first large-scale, randomly generated benchmark dataset for TRS confluence evaluation. Contribution/Results: The framework breaks from traditional hand-crafted strategy paradigms by enabling end-to-end automatic strategy synthesis. It consistently outperforms state-of-the-art manual strategies on both the Cops benchmark and the new dataset, successfully resolving multiple long-standing TRS confluence problems previously unsolved by automated tools. This work establishes a novel paradigm for automation in formal verification and automated reasoning.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Neuro-Symbolic Learning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Term rewriting plays a crucial role in software verification and compiler optimization. With dozens of highly parameterizable techniques developed to prove various system properties, automatic term rewriting tools work in an extensive parameter space. This complexity exceeds human capacity for parameter selection, motivating an investigation into automated strategy invention. In this paper, we focus on confluence, an important property of term rewrite systems, and apply machine learning to develop the first learning-guided automatic confluence prover. Moreover, we randomly generate a large dataset to analyze confluence for term rewrite systems. Our results focus on improving the state-of-the-art automatic confluence prover CSI: When equipped with our invented strategies, it surpasses its human-designed strategies both on the augmented dataset and on the original human-created benchmark dataset Cops, proving/disproving the confluence of several term rewrite systems for which no automated proofs were known before.

Problem

• Automating strategy invention for term rewrite systems
• Improving confluence proofs using machine learning
• Enhancing automatic confluence prover CSI's performance

Innovation

• Machine learning guides confluence proof automation
• Large randomly generated dataset analyzes term rewriting
• Invented strategies outperform human-designed ones