Fully Syntactic Uniform Continuity Formats for Bisimulation Metrics

  • Valentina CastiglioniEmail author
  • Ruggero Lanotte
  • Simone Tini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11760)


Behavioral metrics play a fundamental role in the analysis of probabilistic systems. They allow for a robust comparison of the behavior of processes and provide a formal tool to study their performance, privacy and security properties. Gebler, Larsen and Tini showed that the bisimilarity metric is also suitable for compositional reasoning, expressed in terms of continuity properties of the metric. Moreover, Gebler and Tini provided semantic formats guaranteeing, respectively, the non-extensiveness, non-expansiveness and Lipschitz continuity of this metric. In this paper, starting from their work, we define three specification formats for the bisimilarity metric, one for each continuity property, namely sets of syntactic constraints over the SOS rules defining process operators that guarantee the desired continuity property of the metric.



We thank the anonymous reviewers for their detailed comments and feedback. V. Castiglioni has been partially supported by the project ‘Open Problems in the Equational Logic of Processes’ (OPEL) of the Icelandic Research Fund (grant nr. 196050-051). We thank Carlos, Kostas, Mario and Frank for inviting us to submit this paper. Last but not least, we extend our heartiest wishes to Catuscia. Valentina is indebted to Catuscia for her support, mentoring and friendship during the period spent at INRIA, in her team COMETE. We wish Catuscia a very happy birthday!


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Valentina Castiglioni
    • 1
    • 2
    Email author
  • Ruggero Lanotte
    • 3
  • Simone Tini
    • 3
  1. 1.INRIA Saclay - Ile de FrancePalaiseauFrance
  2. 2.Reykjavik UniversityReykjavikIceland
  3. 3.University of InsubriaComoItaly

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