Almost all partial order reduction techniques proposed for time Petri nets (TPNs in short) are based on the notion of Partially Ordered Sets. The idea is to explore simultaneously, by relaxing some firing order constraints of persistent transitions (An enabled transition is persistent, if it cannot be disabled until its firing.), several equivalent sequences, while computing the convex hull of the abstract states reached by these equivalent sequences. However, unlike timed automata, in the TPN state space abstractions, the union of the abstract states reached by different interleavings of the same set of non conflicting transitions is not necessarily identical to their convex hull. Moreover, the convex hull over-approximation preserves neither the boundedness nor the reachability properties of the TPN. In this context, the main challenge is to establish sufficient conditions over transitions that ensure, in addition to their persistency, identity between the union and the convex hull of the abstract states reachable by their different interleavings. This paper shows how to weaken the sufficient conditions proposed in the literature, by taking into better account the structure, the marking, the static and the dynamic time parameters of the TPN.

中文翻译：

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用于实时系统的延迟相关偏序减少技术

几乎所有针对时间 Petri 网（简称 TPN）提出的偏序约简技术都基于偏序集的概念。这个想法是同时探索，通过放宽持久转换的一些触发顺序约束（一个启用的转换是持久的，如果它在触发之前不能被禁用。），几个等效序列，同时计算这些达到的抽象状态的凸包等效序列。然而，与定时自动机不同的是，在 TPN 状态空间抽象中，同一组非冲突转换的不同交织所达到的抽象状态的并集不一定与其凸包相同。此外，凸包过度近似既不保留 TPN 的有界性，也不保留 TPN 的可达性属性。在这种情况下，主要的挑战是在过渡上建立充分的条件，除了它们的持久性之外，还要确保联合和抽象状态的凸包之间的同一性，这些抽象状态可以通过它们的不同交错实现。本文展示了如何通过更好地考虑 TPN 的结构、标记、静态和动态时间参数来弱化文献中提出的充分条件。