Multiprocessor system on chip (MPSoC) implements system functions through tasks. It is necessary to estimate system behaviors early in the design process without actual hardware implementation. As there are a huge variety in freedom of choices in the mapping of tasks, existing researches mainly focus on the schedulability analysis and resource constraints, with a lack of concerning on how data in tasks “behaves” in different schedulings. In practical applications, tasks are achieved by sequential executions of code blocks, which change the variables accordingly. Some variables are shared by all the tasks through global memory, such as public data, critical signals and so on. Changes of these data reflect functions of the system which also deserves attention. Data dynamics can illustrate data changes within a task as well as data exchanges between tasks, and thus can depict scheduling with more detail than just telling whether they can be scheduled. This paper proposes a new formal approach by combing hybrid automata and probabilistic timed automata to model MPSoC data dynamics, describing its real-time scheduling characteristics, concurrency, and probability. Furthermore, we also propose a new quantitative metric for measuring data dynamics named “reach-ratio” to compute the probability, weighted over tasks, of starting a task from which a certain area of the state space can be reached, where the tasks must be started within a time-bound that varies from task to task. The reach-ratio metric, as a supplement of traditional properties such as safety, liveness and fairness, reflects the extent of which the system achieves the intended function at a given scheduling strategy. Case study investigations of our new formal approach provide empirical evidence for MPSoC designers to balance controller policy without hardware implementation.

中文翻译：

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MPSoC 数据动态的形式验证和量化指标

多处理器片上系统 (MPSoC) 通过任务实现系统功能。在没有实际硬件实现的情况下，有必要在设计过程的早期估计系统行为。由于任务映射的选择自由度很大，现有的研究主要集中在可调度性分析和资源约束上，缺乏对任务中数据在不同调度下的“行为”的关注。在实际应用中，任务是通过代码块的顺序执行来实现的，这些代码块会相应地改变变量。一些变量通过全局内存被所有任务共享，例如公共数据、关键信号等。这些数据的变化反映了系统的功能，也值得关注。数据动态可以说明任务内的数据变化以及任务之间的数据交换，因此可以更详细地描述调度，而不仅仅是告诉它们是否可以调度。本文提出了一种新的形式化方法，将混合自动机和概率定时自动机相结合，对 MPSoC 数据动态进行建模，描述了其实时调度特性、并发性和概率。此外，我们还提出了一种新的量化指标，用于测量数据动态，称为“到达率”，以计算开始任务的概率，加权任务，开始任务可以到达状态空间的某个区域，其中任务必须是在因任务而异的时限内开始。覆盖率指标，作为安全性、活跃性和公平性等传统属性的补充，反映了系统在给定调度策略下实现预期功能的程度。对我们新的形式化方法的案例研究调查为 MPSoC 设计人员在没有硬件实现的情况下平衡控制器策略提供了经验证据。