一句话：将Petri网与事件结构的关系推广到析取因果，用持久库所刻画，并构造与局部连通事件结构的核反射链。
事件结构是并发建模的经典模型。Nielsen、Plotkin 与 Winskel 曾通过展开把安全 Petri 网映射到素事件结构：每个事件有唯一因果集，并可由配置域表示，范畴上形成核反射链。一般事件结构则允许析取因果，即事件可由不同的极小事件集使能。本文将 Petri 网与事件结构的联系扩展到析取因果：在网层面，析取因果由持久库所刻画，其中 token 一旦生成可多次使用而不被消耗，且多个 token 被整体解释、历史无关紧要。作者将普通网的结果推广到带持久性的 Petri 网，借助展开构造将其与一般事件结构的新子类——局部连通事件结构——相联系，并给出相应的核反射链。
Event structures are a well-accepted model of concurrency. In a seminal paper by Nielsen, Plotkin and Winskel, they are used to establish a bridge between the theory of domains and the approach to concurrency proposed by Petri. A basic role is played by an unfolding construction that maps (safe) Petri nets into a subclass of event structures, called prime event structures, where each event has a uniquely determined set of causes. Prime event structures, in turn, can be identified with their domain of configurations. At a categorical level, this is nicely formalised by Winskel as a chain of coreflections. Contrary to prime event structures, general event structures allow for the presence of disjunctive causes, i.e., events can be enabled by distinct minimal sets of events. In this paper, we extend the connection between Petri nets and event structures in order to include disjunctive causes. In particular, we show that, at the level of nets, disjunctive causes are well accounted for by persistent places. These are places where tokens, once generated, can be used several times without being consumed and where multiple tokens are interpreted collectively, i.e., their histories are inessential. Generalising the work on ordinary nets, Petri nets with persistence are related to a new subclass of general event structures, called locally connected, by means of a chain of coreflections relying on an unfolding construction.
@article{paperbot372,
title = {Event Structures for Petri nets with Persistence},
author = {Paolo Baldan and Roberto Bruni and Andrea Corradini and Fabio Gadducci and Hernan Melgratti and Ugo Montanari},
journal = {Logical Methods in Computer Science},
volume = {Volume 14, Issue 3},
year = {2018},
doi = {10.23638/lmcs-14(3:25)2018}
}