Logical Characterization of Bisimulation Metrics
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 t...
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| Vydané v: | Electronic proceedings in theoretical computer science Ročník 227; číslo Proc. QAPL 2016; s. 44 - 62 |
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25.10.2016
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Tini, Simone Gebler, Daniel Castiglioni, Valentina |
| Author_xml | – sequence: 1 givenname: Valentina surname: Castiglioni fullname: Castiglioni, Valentina organization: University of Insubria – sequence: 2 givenname: Daniel surname: Gebler fullname: Gebler, Daniel organization: VU University Amsterdam – sequence: 3 givenname: Simone surname: Tini fullname: Tini, Simone organization: University of Insubria |
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