Open Petri nets
Open Petri nets
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DOI：
10.1017/s0960129520000043
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发表时间：
2020-03-01
影响因子：
0.5
通讯作者：
Master, Jade
中科院分区：
文献类型：
--
作者：
Baez, John C.;Master, Jade
Petri网的可达性语义可以用开放的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空间将某些地方指定为输入和输出的网。我们可以通过将一个的输出与另一个的输入粘合在一起来组成开放的Petri网。开Petri网可以看作是一个开（Petri）范畴的态射，它在不相交并下变成对称一元。然而，由于开放Petri网的复合仅被定义为同构，因此最好将它们视为对称单一性双范畴open （Petri）的态射。我们描述了开放Petri网的两种语义形式，使用open （Petri）外的对称单系双函子。第一个是操作语义，它为每个开放的Petri网给出一个范畴，这个范畴的态射是这个网可以执行的过程。这是以组合的方式完成的，因此这些类别可以在较小的子网上计算，然后粘合在一起。第二种是可达性语义，它简单地表示可以从给定的输入标记到达输出的哪些标记。
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 Open(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 Open(Petri). We describe two forms of semantics for open Petri nets using symmetric monoidal double functors out of Open(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.