Causality versus True Concurrency in the Setting of Real-Time Models
The contribution of the paper is to clarify connections between real-time models of concurrency. In particular, we deﬁned a category of timed causal trees and investigated how it relates to other categories of timed models. Moreover, using a larger model called timed event trees, we constructed an adjunction from the category of timed causal trees to the category of timed event structures. Thereby we showed that timed causal trees are more trivial than timed event structures because they reﬂect only one aspect of true concurrency, causality, and they apply causality without a notion of event. On the other hand, the ﬁrst model is more expressive than the latter in that possible runs of a timed causal tree can be deﬁned in terms of a tree without restrictions, but the set of the possible runs of any event structure must be closed under the shuﬄing of concurrent transitions.