This paper proposes a semi-structural approach to verify the nonblockingness of a Petri net. We provide an algorithm to construct a novel structure, called minimax basis reachability graph (minimax-BRG): it provides an abstract description of the reachability set of a net while preserving all information needed to test if the net is blocking. We prove that a bounded deadlock-free Petri net is nonblocking if and only if its minimax-BRG is unobstructed, which can be verified by solving a set of integer linear programming problems (ILPPs). For Petri nets that are not deadlock-free, one needs to determine the set of deadlock markings. This can be done with an efficient approach based on the computation of maximal implicit firing sequences enabled by the markings in the minimax-BRG. The approach we developed does not require exhaustive exploration of the state space and therefore achieves significant practical efficiency, as shown by means of numerical simulations.

中文翻译：

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验证有界 Petri 网中的非阻塞性：一种新颖的半结构化方法

本文提出了一种半结构化方法来验证 Petri 网的非阻塞性。我们提供了一种构建新结构的算法，称为极小极大基可达图（minimax-BRG）：它提供了网络可达集的抽象描述，同时保留了测试网络是否阻塞所需的所有信息。我们证明了一个有界无死锁 Petri 网是非阻塞的，当且仅当它的 minimax-BRG 是无障碍的，这可以通过解决一组整数线性规划问题 (ILPPs) 来验证。对于非无死锁的 Petri 网，需要确定一组死锁标记。这可以通过基于由 minimax-BRG 中的标记启用的最大隐式点火序列的计算的有效方法来完成。