This paper studies the verification and enforcement of deadlock-freeness and liveness in partially controllable Petri nets. First, we introduce a particular type of basis reachability graphs called (CFCE-BRGs), in which the firings of all structurally conflicting transitions and all controllable ones are explicitly encoded. We propose two sufficient and necessary conditions for verifying deadlock-freeness and liveness of a Petri net; both can be verified by inspecting a CFCE-BRG using graph theory. Moreover, we develop two maximally permissive deadlock-freeness and liveness enforcing supervisors based on the trimming of CFCE-BRGs. The developed approaches are applicable to arbitrary bounded Petri nets, without an exhaustive reachability space enumeration.

中文翻译：

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使用基础可达性图在有界 Petri 网中验证和执行活性和无死锁

本文研究了部分可控 Petri 网中无死锁和活性的验证和执行。首先，我们引入一种称为（CFCE-BRG）的特殊类型的基础可达性图，其中所有结构冲突的转换和所有可控转换的激发都被显式编码。我们提出了两个充分必要条件来验证 Petri 网的无死锁性和活性；两者都可以通过使用图论检查 CFCE-BRG 来验证。此外，我们基于 CFCE-BRG 的修剪开发了两个最大允许的无死锁和活性执行监督程序。所开发的方法适用于任意有界 Petri 网，无需详尽的可达性空间枚举。