An Intrinsic Characterization of Approximate Probabilistic Bisimulation
Franck van Breugel, Michael Mislove, Joel Ouaknine and James Worrell
Technical Report CS-2003-01
York University
January 2003
Abstract
In previous work we have investigated a notion of approximate bisimilarity for labelled Markov processes. We argued that such a notion is more realistic and more feasible to compute than (exact) bisimilarity. The main technical tool used in the underlying theory was the Hutchinson metric on probability measures. This paper gives a more fundamental characterization of approximate bisimilarity in terms of the notion of (exact) similarity. In particular, we show that the topology of approximate bisimilarity is the Lawson topology with respect to the simulation preorder. To complement this abstract characterization we give a statistical account of similarity, and by extension, of approximate bisimilarity, in terms of the process testing formalism of Larsen and Skou.
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