A Reversible perspective on Petri Nets and event structures

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 postset and preset of transitions. In this way, we are able to operationally explain the full model of reversible prime event structures.