Published in Volume XXXII, Issue 2, 2022, pages 211-254, doi: 10.7561/SACS.2022.2.211

Authors: W. Du, Y. Deng, D. Gebler


For the model of probabilistic labelled transition systems that allow for the co-existence of nondeterminism and probabilities, we present two notions of bisimulation metrics: one is state-based and the other is distribution-based. We provide a sound and complete modal characterisation for each of them, using real-valued modal logics based on Hennessy-Milner logic. The logic for characterising the state-based metric is much simpler than an earlier logic proposed by Desharnais et al. as it uses only two non-expansive operators rather than the general class of non-expansive operators. For the kernels of the two metrics, which correspond to two notions of bisimilarity, we give a comprehensive comparison with some typical distribution-based bisimilarities in the literature.

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  title={Behavioural Pseudometrics for Nondeterministic Probabilistic Systems},
  author={W. Du, Y. Deng, D. Gebler},
  journal={Scientific Annals of Computer Science},
  organization={Alexandru Ioan Cuza University, Ia\c si, Rom\^ania},
  publisher={Alexandru Ioan Cuza University Press, Ia\c si},