🤖 AI Summary
Reversible concurrent models lack a unified semantic foundation.
Method: We introduce the first category of reversible causal nets featuring asymmetric conflict and establish a strict categorical isomorphism between this category and that of reversible asymmetric event structures. Our approach extends classical causal nets to accommodate asymmetric conflict, constructs a categorical semantics for their reversible variants, and formally proves equivalence between the two reversible models using category theory, Petri net theory, and event structure semantics.
Contribution/Results: This work achieves the first precise categorical correspondence between reversible Petri nets and reversible event structures. It provides a unifying semantic foundation for reversible distributed systems, a formal model-transformation framework, and rigorous grounds for verification. The isomorphism ensures structural and behavioral equivalence, enabling cross-paradigm reasoning and tool interoperability in reversible computing.
📝 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.