Real-Time Stable Event Structures And Marked Scott Domains: An Adjunction

Event structures constitute a major branch of models for concurrency. Their advantage is that they explicitly exhibit the interplay between concurrency and nondeterminism. In a seminal work, Winskel has shown that categories of prime and stable event structures can be related to a category of Scott domains by adjunctions. The intention of this note is to show the applicability of the theory-categorical framework to a real-time extension of stable event structures, in order to identify suitable semantical domains for the models. To that end, we first introduce a category TSES of real-time stable event structures, and a category MDom of a particular class of Scott domains, called marked Scott domains, and then define an adjunction between TSES and MDom.