Model checkers for timed automata are widely used to verify safety-critical, real-time systems. State-of-the-art tools achieve scalability by intricate abstractions. We aim at further increasing the trust in their verification results, in particular for checking liveness properties. To this end, we develop an approach for extracting certificates for the emptiness of timed B\"uchi automata from model checking runs. These certificates can be double-checked by a certifier that we formally verify in Isabelle/HOL. We study liveness certificates in an abstract setting and show that our approach is sound and complete. To also demonstrate its feasibility, we extract certificates for several models checked by TChecker and Imitator, and validate them with our verified certifier.

中文翻译：

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证明定时 B\"uchi Automata 是空的

定时自动机的模型检查器被广泛用于验证安全关键的实时系统。最先进的工具通过复杂的抽象实现可扩展性。我们的目标是进一步提高对其验证结果的信任，特别是在检查活性属性方面。为此，我们开发了一种从模型检查运行中提取定时 B\"uchi 自动机的空性证书的方法。这些证书可以由我们在 Isabelle/HOL 中正式验证的证明者进行双重检查。我们在一个抽象的设置，表明我们的方法是合理和完整的。为了证明其可行性，我们提取了由 TChecker 和 Imitator 检查的几个模型的证书，并与我们经过验证的验证者进行验证。