LLM-Powered Automatic Theorem Proving and Synthesis for Hybrid Systems and Game

2026-02-28

AI Summary

This work addresses the formidable challenge of formal verification and controller synthesis for hybrid systems and games, where the tight coupling of discrete control and continuous dynamics exceeds the capabilities of traditional automated theorem proving methods. For the first time, large language models (LLMs) are integrated into this domain, leveraging the highly expressive differential game logic (dGL) as a formal foundation. By combining LLM-driven interactive theorem proving with dGL, the approach enables automated verification and strategy synthesis. It overcomes the scalability limitations of existing techniques in complex cyber-physical systems, successfully verifying all five challenging benchmarks that surpass the capacity of current automated tools, and synthesizing correct control strategies in four of them.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Multiagent Systems: Adversarial Agents

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

Abstract

Hybrid games model cyber-physical systems (CPS), like cars, trains, and airplanes, where discrete control decisions interact with continuous physical dynamics. We use Large Language Models (LLMs) to scale formal verification and synthesis for hybrid systems and games for a high-level hybrid games symbolic logic, differential game logic (dGL). This combination of a logic with the right expressivity and automation of the interactive theorem proving process using LLMs brings within reach a challenging class of CPS verification/synthesis problems, that were previously well out of range of automatic theorem proving. We demonstrate it on five challenging case studies, all beyond the reach of existing automatic techniques. Verification succeeds for all five, and the synthesis of control solutions succeeds for four of the five.

Problem

• hybrid systems
• cyber-physical systems
• automatic theorem proving
• formal verification
• control synthesis

Innovation

• Large Language Models
• differential game logic
• hybrid systems
• automatic theorem proving
• cyber-physical systems