Causality Versus True-Concurrency

Category theory has been successfully employed to structure the confusing setup of models and equivalences for concurrency: Winskel and Nielsen have related the standard models nctions and (co)reflections while Joyal et al. have defined an abstract notion of equivalence, known as open map bisimilarity. One model has not been integrated into this framework: the causal trees of Darondeau and Degano. Here we fill this gap. In particular, we show that there is an adjunction from causal trees to event structures, which we bring to light via a mediating model, that of event trees. Further, we achieve an open map characterization of history preserving bisimilarity: the latter is captured by the natural ation of the abstract bisimilarity for causal trees. Key words: event structures, causal trees, bisimulation In [6] Winskel and Nielsen employ category theory to relate and unify the many models for concurrency. The basic idea is to represent models as categories: each model is equipped with a...

• Type: Journal
• Year: 2006
• Where: ENTCS
• Authors: Sibylle B. Fröschle, Slawomir Lasota
• Keywords: Category Theory, Causal Trees, ENTCS 2006, Joyal Et Al