Vector addition systems (VAS), also known as Petri nets, are a popular model of concurrent systems. Many problems from many areas reduce to the reachability problem for VAS, which consists of deciding whether a target configuration of a VAS is reachable from a given initial configuration. One of the main approaches to solve the problem on practical instances is called flattening, intuitively removing nested loops. This technique is known to terminate for semilinear VAS. In this paper, we prove that also for VAS with nested zero tests, called Priority VAS, flattening does in fact terminate for all semilinear reachability relations. Furthermore, we prove that Priority VAS admit semilinear inductive invariants. Both of these results are obtained by defining a well-quasi-order on runs of Priority VAS which has good pumping properties.

中文翻译：

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优先向量加法系统的平坦性

矢量加法系统 (VAS)，也称为 Petri 网，是并发系统的流行模型。来自许多领域的许多问题都归结为VAS的可达性问题，其中包括确定VAS的目标配置是否可以从给定的初始配置到达。解决实际实例问题的主要方法之一称为扁平化，直观地删除嵌套循环。众所周知，该技术会终止半线性 VAS。在本文中，我们证明对于具有嵌套零测试的 VAS（称为优先级 VAS），平坦化实际上会终止所有半线性可达关系。此外，我们证明了优先级VAS允许半线性归纳不变量。这两个结果都是通过在具有良好泵送特性的 Priority VAS 运行上定义井准阶而获得的。