Event structures have emerged as a foundational model for concurrent computation, explaining computational processes by outlining the events and the relationships that dictate their execution. They play a pivotal role in the study of key aspects of concurrent computation models, such as causality and independence, and have found applications across a broad range of languages and models, spanning realms like persistence, probabilities, and quantum computing. Recently, event structures have been extended to address reversibility, where computational processes can undo previous computations. In this context, reversible event structures provide abstract representations of processes capable of both forward and backward steps in a computation. Since their introduction, event structures have played a crucial role in bridging operational models, traditionally exemplified by Petri nets and process calculi, with denotational ones, i.e., algebraic domains. In this context, we revisit the standard connection between Petri nets and event structures under the lenses of reversibility. Specifically, we introduce a subset of contextual Petri nets, dubbed reversible causal nets, that precisely correspond to reversible prime event structures. The distinctive feature of reversible causal nets lies in deriving causality from inhibitor arcs, departing from the conventional dependence on the overlap between the post and preset of transitions. In this way, we are able to operationally explain the full model of reversible prime event structures.

翻译：事件结构已成为并发计算的基础模型，通过描述事件及其执行关系来阐释计算过程。它们在并发计算模型的关键特性（如因果性与独立性）研究中发挥着核心作用，并已广泛应用于持久性、概率论与量子计算等领域的多种语言和模型。近期，事件结构被扩展以支持可逆性——即计算过程能够撤销先前操作的能力。在此背景下，可逆事件结构为具备前向与后向计算能力的进程提供了抽象表示。自提出以来，事件结构在连接操作模型（典型如佩特里网与进程演算）与指称模型（即代数域）中扮演关键角色。本文重新审视了佩特里网与事件结构在可逆性框架下的标准关联，具体而言，我们引入了上下文佩特里网的一个子类——可逆因果网，该类网络恰好对应于可逆素事件结构。可逆因果网的独特之处在于：它通过抑制弧推导因果关系，而非依赖传统中变迁后集与前集的重叠。由此，我们得以从操作层面完整解释可逆素事件结构模型。