Acta Informatica

, Volume 55, Issue 6, pp 489–520 | Cite as

Replication, refinement & reachability: complexity in dynamic condition-response graphs

  • Søren DeboisEmail author
  • Thomas T. Hildebrandt
  • Tijs Slaats
Original Article


We explore the complexity of reachability and run-time refinement under safety and liveness constraints in event-based process models. Our study is framed in the DCR\(^\star \) process language, which supports modular specification through a compositional operational semantics. DCR\(^\star \) encompasses the “Dynamic Condition Response (DCR) graphs” declarative process model for analysis, execution and safe run-time refinement of process-aware information systems; including replication of sub-processes. We prove that event-reachability and refinement are np-hard for DCR\(^\star \) processes without replication, and that these finite state processes recognise exactly the languages that are the union of a regular and an \(\omega \)-regular language. Moreover, we prove that event-reachability and refinement are undecidable in general for DCR\(^\star \) processes with replication and local events, and we provide a tractable approximation for refinement. A prototype implementation of the DCR\(^\star \) language is available at


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© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceIT University of CopenhagenCopenhagen SDenmark
  2. 2.Department of Computer ScienceUniversity of CopenhagenCopenhagen SDenmark

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