开放Petri网
Open Petri Nets
摘要：
Petri网的可达性语义可以用开放Petri网来研究。对我们来说，一个“开放”的Petri网是一个通过集合的余跨度指定为输入和输出的某些地方。我们可以通过将一个Petri网的输出粘到另一个Petri网的输入来组成开放Petri网。开放Petri网可以看作是范畴$\mathsf{Open}(\mathsf{Petri})$的态射，它在不交并下成为对称幺半群.然而，由于开放Petri网的复合仅定义为同构，因此最好将它们视为对称monoidal双范畴$\mathbb{O}\mathbf{pen}(\mathsf{Petri})$的态射。我们描述了两种形式的语义开放Petri网使用对称monoidal双函子的$\mathbb{O}\mathbf{pen}(\mathsf{Petri})$。第一，一个操作语义，给每个开放的Petri网的范畴，其态射是这个网可以进行的过程。这是以组合的方式完成的，因此这些类别可以在较小的数组上计算，然后粘在一起。第二种是可达性语义，它简单地说，从输入的给定标记可以到达输出的哪些标记。
英文摘要：
The reachability semantics for Petri nets can be studied using open Petri nets. For us an "open" Petri net is one with certain places designated as inputs and outputs via a cospan of sets. We can compose open Petri nets by gluing the outputs of one to the inputs of another. Open Petri nets can be treated as morphisms of a category $\mathsf{Open}(\mathsf{Petri})$, which becomes symmetric monoidal under disjoint union. However, since the composite of open Petri nets is defined only up to isomorphism, it is better to treat them as morphisms of a symmetric monoidal double category $\mathbb{O}\mathbf{pen}(\mathsf{Petri})$. We describe two forms of semantics for open Petri nets using symmetric monoidal double functors out of $\mathbb{O}\mathbf{pen}(\mathsf{Petri})$. The first, an operational semantics, gives for each open Petri net a category whose morphisms are the processes that this net can carry out. This is done in a compositional way, so that these categories can be computed on smaller subnets and then glued together. The second, a reachability semantics, simply says which markings of the outputs can be reached from a given marking of the inputs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
