Generalized Bisimulation Metrics

Abstract

The pseudometric based on the Kantorovich lifting is one of the most popular notion of distance between probabilistic processes proposed in the literature. However, its application in verification is limited to linear properties. We propose a generalization which allows to deal with a wider class of properties, such as those used in security and privacy. More precisely, we propose a family of pseudometrics, parametrized on a notion of distance which depends on the property we want to verify. Furthermore, we show that the members of this family still characterize bisimilarity in terms of their kernel, and provide a bound on the corresponding distance between trace distributions. Finally, we study the instance corresponding to differential privacy, and we show that it has a dual form, easier to compute. We also prove that the typical processalgebra constructs are non-expansive, thus paving the way to a modular approach to verification.

Bisimilarity Distances for Approximate Differential Privacy

“…For instance, the distance between any bisimilar states turns out to be zero. In contrast to [12], the converse will not hold. Example 1.…”

“…∆ 2 is not a pseudometric 3 . This will complicate our technical development, because we will not be able to use the framework of [12] directly.…”

“…Our distance will be defined in the spirit of bisimilarity distances [12,14,16,17] through a fixed point definition based on a variation of the Kantorovich lifting. To motivate its shape, let us discuss how one would go about calculating tv α recursively.…”

“…Hutchinson, Wasserstein distance), having been rediscovered several times in history [15]. Chatzikokolakis et al [12] studied the Kantorovich distance and related bisimulation distances when the absolute value distance above is replaced with another metric. For our purposes, instead of |...|, we need to consider ∆ α , even though ∆ α is not a metric and m may not be a pseudometric.…”

Modelling and Analysis of Network Security - a Probabilistic Value-passing CCS Approach

“…For describing and analyzing cryptographic protocols, the spi calculus, an extension of the π calculus, was designed [1]. Recently, a generalization of the bisimilarity pseudo-metric based on the Kantorovich lifting is proposed, this metric allows to deal with a wider class of properties such as those used in security and privacy [3].…”