# Relating Reversible Petri Nets and Reversible Event Structures, categorically

## TL;DR

This paper explores the categorical relationships between reversible Petri nets with asymmetric conflicts and reversible event structures, extending causal nets to better model concurrent, distributed, and reversible systems.

## Contribution

It introduces a categorical framework for reversible causal nets with asymmetric conflicts and relates them to reversible asymmetric event structures.

## Key findings

- Extended causal nets to include asymmetric conflicts
- Established categorical relationships between nets and event structures
- Provided a formal foundation for reversible concurrent systems

## Abstract

Causal nets (CNs) are Petri nets where causal dependencies are modelled via inhibitor arcs. They play the role of occurrence nets when representing the behaviour of a concurrent and distributed system, even when reversibility is considered. In this paper we extend CNs to account also for asymmetric conflicts and study (i) how this kind of nets, and their reversible versions, can be turned into a category; and (ii) their relation with the categories of reversible asymmetric event structures.