Logical Characterization of Bisimulation Metrics

Valentina Castiglioni
(University of Insubria)
Daniel Gebler
(VU University Amsterdam)
Simone Tini
(University of Insubria)

Bisimulation metrics provide a robust and accurate approach to study the behavior of nondeterministic probabilistic processes. In this paper, we propose a logical characterization of bisimulation metrics based on a simple probabilistic variant of the Hennessy-Milner logic. Our approach is based on the novel notions of mimicking formulae and distance between formulae. The former are a weak version of the well known characteristic formulae and allow us to characterize also (ready) probabilistic simulation and probabilistic bisimilarity. The latter is a 1-bounded pseudometric on formulae that mirrors the Hausdorff and Kantorovich lifting the defining bisimilarity pseudometric. We show that the distance between two processes equals the distance between their own mimicking formulae.

In Mirco Tribastone and Herbert Wiklicky: Proceedings 14th International Workshop Quantitative Aspects of Programming Languages and Systems (QAPL'16), Eindhoven, The Netherlands, April 2-3, 2016, Electronic Proceedings in Theoretical Computer Science 227, pp. 44–62.
Published: 25th October 2016.

ArXived at: https://dx.doi.org/10.4204/EPTCS.227.4 bibtex PDF
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