Event-B is a formal method that utilizes a stepwise development approach for system-level modeling and analysis. We are interested in reasoning about real-time deadlines and delays between trigger and response events. There is existing work on treating these properties in Event-B but it lacks a semantic treatment in terms of trace behaviors. Because timing properties require fairness assumptions, we use infinite traces and develop conditions under which all infinite traces of a machine satisfy trigger-response and timing properties. We present refinement semantics of models whose behavior traces are infinite. In addition, we generalize our previous work by allowing a relation between concrete states and abstract states to simulate infinite state traces. Forward simulation, which is a proof technique for refinement, has been used to verify the consistency between different refinement levels regarding finite traces. Based on forward simulation, fairness assumptions, relative deadlock freedom, and conditional convergence are adopted as additional conditions that guarantee infinite trace refinement of timed models. The bounded retransmission protocol is used to illustrate the required proof obligations for timed traces.

Event-B是一种正式方法，它采用逐步开发方法进行系统级建模和分析。我们对推理的实时期限和触发事件与响应事件之间的延迟感兴趣。在事件B中有处理这些属性的现有工作，但是在跟踪行为方面缺乏语义处理。因为时序属性需要公平性假设，所以我们使用无穷迹线，并开发了一种条件，在该条件下，机器的所有无穷迹线都满足触发响应和时序属性。我们提出了行为痕迹是无限的模型的细化语义。另外，我们通过允许具体状态和抽象状态之间的关系模拟无限状态轨迹来概括我们以前的工作。正向仿真是一种完善的证明技术，已用于验证关于有限迹线的不同细化级别之间的一致性。在前向仿真的基础上，采用公平性假设，相对死锁自由和条件收敛作为附加条件，以保证对定时模型进行无穷细化。有界重传协议用于说明定时跟踪所需的证明义务。