Petri网的两种多图表示
Two polygraphic presentations of Petri nets
摘要：
本文给出了Petri网的一个代数和两个多图翻译，所有三个都提供了一种更简单的方法来描述约简并识别其中的一些。第一种将位置视为交换幺半群的生成元，将变迁视为其上的重写规则：这种设置完全等同于Petri网，但缺乏任何图形直观性。第二种把地点看作是一维的细胞，把过渡看作是二维的：这种翻译恢复了图形的意义，但由于它使用了显式的排列，因此带来了许多困难。最后，第三种翻译将地点视为退化的2维细胞，将变迁视为3维细胞：这是一种等同于Petri网的设置，配备了图形解释。
英文摘要：
This document gives an algebraic and two polygraphic translations of Petri nets, all three providing an easier way to describe reductions and to identify some of them. The first one sees places as generators of a commutative monoid and transitions as rewriting rules on it: this setting is totally equivalent to Petri nets, but lacks any graphical intuition. The second one considers places as 1-dimensional cells and transitions as 2-dimensional ones: this translation recovers a graphical meaning but raises many difficulties since it uses explicit permutations. Finally, the third translation sees places as degenerated 2-dimensional cells and transitions as 3-dimensional ones: this is a setting equivalent to Petri nets, equipped with a graphical interpretation.
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。
