Conditional Bisimilarity for Reactive Systems

Authors Mathias Hülsbusch, Barbara König, Sebastian Küpper, Lara Stoltenow

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Mathias Hülsbusch
  • Universität Duisburg-Essen, Germany
Barbara König
  • Universität Duisburg-Essen, Germany
Sebastian Küpper
  • FernUniversität in Hagen, Germany
Lara Stoltenow
  • Universität Duisburg-Essen, Germany

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Mathias Hülsbusch, Barbara König, Sebastian Küpper, and Lara Stoltenow. Conditional Bisimilarity for Reactive Systems. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Reactive systems à la Leifer and Milner, an abstract categorical framework for rewriting, provide a suitable framework for deriving bisimulation congruences. This is done by synthesizing interactions with the environment in order to obtain a compositional semantics. We enrich the notion of reactive systems by conditions on two levels: first, as in earlier work, we consider rules enriched with application conditions and second, we investigate the notion of conditional bisimilarity. Conditional bisimilarity allows us to say that two system states are bisimilar provided that the environment satisfies a given condition. We present several equivalent definitions of conditional bisimilarity, including one that is useful for concrete proofs and that employs an up-to-context technique, and we compare with related behavioural equivalences. We instantiate reactive systems in order to obtain DPO graph rewriting and consider a case study in this setting.

Subject Classification

ACM Subject Classification
  • Theory of computation → Concurrency
  • Theory of computation → Program reasoning
  • conditional bisimilarity
  • reactive systems
  • up-to context
  • graph transformation


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