A Learner-Refiner Framework for Barrier Certificate Generation

Barrier certificate is a powerful tool for verifying they safety property of dynamical systems. In this paper, we introduce an innovative learner–refiner framework for synthesizing polynomial barrier certificates. The framework comprises a learner and a refiner, which work inductively to generate barrier certificates. More specifically, the learner trains barrier certificate candidates represented by feedforward neural networks with polynomial activations, while the refiner utilizes sums of squares (SOS) programming to either validate the candidates or recover valid barrier certificates. Our framework achieves great efficiency via supervised learning, and it ensures formal soundness using SOS-based verification. We implement the LR4BC tool, and we perform a comprehensive experimental evaluation using several benchmarks. The results demonstrate that our tool not only successfully synthesizes polynomial barrier certificates undetected via the SOS-based tool PRoTECT but also achieves a significant speedup in efficiency compared to the neural network-based tool FOSSIL 2.0.