一句话：为 P/T Petri 网提出基于展开的因果可逆语义，并用带因果历史颜色的有限网表示其可逆行为。
Petri 网是经典的并发模型，但一直缺乏令人满意的因果可逆语义。本文为位置/变迁（P/T）Petri 网提出因果可逆语义，其基础有两点：显式表达事件间因果与冲突的发生网（occurrence net）可通过为每个前向变迁添加逆向变迁来直接反转；而 P/T 网经标准展开构造可得到保持全部计算的发生网。因此，P/T 网的可逆语义可由其展开的可逆语义得到。作者进一步表明，这种可逆行为可表示为一个有限网，其 token 由因果历史着色；这些颜色类似于可逆进程演算中典型的因果记忆。
Petri nets are a well-known model of concurrency and provide an ideal setting for the study of fundamental aspects in concurrent systems. Despite their simplicity, they still lack a satisfactory causally reversible semantics. We develop such semantics for Place/Transitions Petri nets (P/T nets) based on two observations. Firstly, a net that explicitly expresses causality and conflict among events, for example an occurrence net, can be straightforwardly reversed by adding a reverse transition for each of its forward transitions. Secondly, given a P/T net the standard unfolding construction associates with it an occurrence net that preserves all of its computation. Consequently, the reversible semantics of a P/T net can be obtained as the reversible semantics of its unfolding. We show that such reversible behaviour can be expressed as a finite net whose tokens are coloured by causal histories. Colours in our encoding resemble the causal memories that are typical in reversible process calculi.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{MelgrattiMU20,
title = {Reversing Place Transition Nets},
author = {Hernán Melgratti and Claudio Antares Mezzina and Irek Ulidowski},
journal = {Logical Methods in Computer Science},
volume = {Volume 16, Issue 4},
year = {2020},
doi = {10.23638/lmcs-16(4:5)2020}
}