Continuous invariants are an important component in deductive verification of hybrid and continuous systems. Just like discrete invariants are used to reason about correctness in discrete systems without having to unroll their loops, continuous invariants are used to reason about differential equations without having to solve them. Automatic generation of continuous invariants remains one of the biggest practical challenges to the automation of formal proofs of safety for hybrid systems. There are at present many disparate methods available for generating continuous invariants; however, this wealth of diverse techniques presents a number of challenges, with different methods having different strengths and weaknesses. To address some of these challenges, we develop Pegasus: an automatic continuous invariant generator which allows for combinations of various methods, and integrate it with the KeYmaera X theorem prover for hybrid systems. We describe some of the architectural aspects of this integration, comment on its methods and challenges, and present an experimental evaluation on a suite of benchmarks.

中文翻译：

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Pegasus：声音连续不变生成

连续不变量是混合和连续系统演绎验证的重要组成部分。就像离散不变量用于推理离散系统中的正确性而无需展开其循环一样，连续不变量用于推理微分方程而无需求解它们。自动生成连续不变量仍然是混合系统形式安全证明自动化的最大实际挑战之一。目前有许多不同的方法可用于生成连续不变量；然而，这种丰富多样的技术带来了许多挑战，不同的方法具有不同的优势和劣势。为了应对其中一些挑战，我们开发了 Pegasus：一个自动连续不变量生成器，允许组合各种方法，并将其与混合系统的 KeYmaera X 定理证明器集成。我们描述了这种集成的一些架构方面，评论了它的方法和挑战，并对一套基准进行了实验评估。