Causality versus true-concurrency

  • Authors:
  • Sibylle Fröschle;Sawomir Lasota

  • Affiliations:
  • Department of Computing Science, University of Oldenburg, 26111 Oldenburg, Germany;Institute of Informatics, Warsaw University, 02-097 Warszawa, Banacha 2, Poland

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2007

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Abstract

Category theory has been successfully employed to structure the confusing set-up of models and equivalences for concurrency: Winskel and Nielsen have related the standard models via adjunctions 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 instantiation of the abstract bisimilarity for causal trees.