A marked Petri net is lucent if there are no two different reachable markings enabling the same set of transitions, i.e., states are fully characterized by the transitions they enable. Characterizing the class of systems that are lucent is a foundational and also challenging question. However, little research has been done on the topic. In this paper, it is shown that all free-choice nets having a home cluster are lucent. These nets have a so-called home marking such that it is always possible to reach this marking again. Such a home marking can serve as a regeneration point or as an end-point. The result is highly relevant because in many applications, we want the system to be lucent and many well-behaved process models fall into the class identified in this paper. Unlike previous work, we do not require the marked Petri net to be live and strongly connected. Most of the analysis techniques for free-choice nets are tailored towards well-formed nets. The approach presented in this paper provides a novel perspective enabling new analysis techniques for free-choice nets that do not need to be well-formed. Therefore, we can also model systems and processes that are terminating and/or have an initialization phase.

中文翻译：

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具有家庭集群的自由选择网络是 Lucent

如果没有两个不同的可达标记启用同一组转换，即状态完全由它们启用的转换表征，则标记的 Petri 网是透明的。表征透明的系统类别是一个基本且具有挑战性的问题。然而，关于该主题的研究很少。在本文中，表明所有具有家庭簇的自由选择网都是透明的。这些网有一个所谓的主场标记，这样总是有可能再次到达这个标记。这种家庭标记可以作为再生点或终点。结果是高度相关的，因为在许多应用程序中，我们希望系统是透明的，并且许多行为良好的过程模型都属于本文中确定的类别。不同于以往的作品，我们不要求标记的 Petri 网是活跃的和强连接的。大多数自由选择网络的分析技术都是针对格式良好的网络量身定制的。本文提出的方法提供了一个新的视角，为不需要格式良好的自由选择网络提供了新的分析技术。因此，我们还可以对正在终止和/或具有初始化阶段的系统和进程进行建模。