An intrinsic characterization of approximate probabilistic bisimilarity

Authors:
Franck van Breugel;Michael Mislove;Joël Ouaknine;James Worrell
Affiliations:
York University, Department of Computer Science, Toronto, Canada;Tulane University, Department of Mathematics, New Orleans, LA;Computer Science Department, Carnegie Mellon University, Pittsburgh, PA;Tulane University, Department of Mathematics, New Orleans, LA
Venue:
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
Year:
2003

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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.