Time-Sensitive Distributed Systems (TSDS), such as applications using autonomous drones, achieve goals under possible environment interference (\eg, winds). Moreover, goals are often specified using explicit time constraints which must be satisfied by the system \emph{perpetually}. For example, drones carrying out the surveillance of some area must always have \emph{recent pictures}, \ie, at most $M$ time units old, of some strategic locations. This paper proposes a Multiset Rewriting language with explicit time for specifying and analysing TSDSes. We introduce two properties, \emph{realizability} (some trace is good) and \emph{survivability} (where, in addition, all admissible traces are good). A good trace is an infinite trace in which goals are perpetually satisfied. We propose a class of systems called \emph{progressive timed systems} (PTS), where intuitively only a finite number of actions can be carried out in a bounded time period. We prove that for this class of systems both the realizability and the survivability problems are PSPACE-complete. Furthermore, if we impose a bound on time (as in bounded model-checking), we show that for PTS, realizability becomes NP-complete, while survivability is in the $\Delta_2^p$ class of the polynomial hierarchy. Finally, we demonstrate that the rewriting logic system Maude can be used to automate time bounded verification of PTS.

翻译：时间敏感分布式系统（TSDS），例如使用自主无人机的应用，需在可能的环境干扰（如风力）下实现目标。此外，目标通常通过显式时间约束来规定，且系统必须持续满足这些约束。例如，执行区域监视任务的无人机必须始终拥有某些关键位置的最新照片，即照片的时效性不得超过 $M$ 个时间单位。本文提出一种带显式时间的多重集重写语言，用于规约与分析 TSDS。我们引入了两个属性：可实现性（存在一条良性轨迹）与可存续性（在此基础上，所有可容许轨迹均为良性）。良性轨迹是指目标被持续满足的无限轨迹。我们提出一类称为渐进时序系统的系统模型，其直观特征是在有限时间段内仅能执行有限数量的动作。我们证明对于此类系统，可实现性与可存续性判定问题均为 PSPACE 完全问题。进一步地，若对时间施加界限（如有界模型检测），我们证明对于渐进时序系统，可实现性问题将变为 NP 完全问题，而可存续性问题则属于多项式层次结构的 $\Delta_2^p$ 类。最后，我们论证了重写逻辑系统 Maude 可用于实现渐进时序系统的时间有界验证自动化。