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An Intrinsic Characterization of Approximate Probabilistic Bisimilarity
 In: Proceedings of FOSSACS 03. LNCS
, 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 o ..."
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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. 1
Testing probabilistic equivalence through reinforcement learning
 In Proceedings of the 26th Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS
, 2006
"... Abstract. We propose a new approach to verification of probabilistic processes for which the model may not be available. We use a technique from Reinforcement Learning to approximate how far apart two processes are by solving a Markov Decision Process. If two processes are equivalent, the algorithm ..."
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Abstract. We propose a new approach to verification of probabilistic processes for which the model may not be available. We use a technique from Reinforcement Learning to approximate how far apart two processes are by solving a Markov Decision Process. If two processes are equivalent, the algorithm will return zero, otherwise it will provide a number and a test that witness the non equivalence. We suggest a new family of equivalences, called Kmoment, for which it is possible to do so. The weakest, 1moment equivalence, is traceequivalence. The others are weaker than bisimulation but stronger than traceequivalence. 1
Testing stochastic processes through reinforcement learning
 In NIPS Workshop on Testing of Deployable Learning and Decision Systems
, 2006
"... We propose a new approach to verification of probabilistic processes for which the model may not be available. We show how to use a technique from Reinforcement Learning to approximate how far apart two processes are by solving a Markov Decision Process. The key idea of the approach is to define the ..."
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Cited by 1 (0 self)
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We propose a new approach to verification of probabilistic processes for which the model may not be available. We show how to use a technique from Reinforcement Learning to approximate how far apart two processes are by solving a Markov Decision Process. The key idea of the approach is to define the MDP out of the processes to be tested, in such a way that the optimal value is interpreted as a divergence between the processes. This divergence can therefore be estimated by Reinforcement Learning methods; moreover, if the two systems are not equivalent, the algorithm returns the test(s) witnessing the nonequivalence. We show how the approach can be adapted to (1) several equivalence notions (trace, ready, etc.) but more importantly to (2) other stochastic formalisms, in particular to MDPs themselves. 1
Testing for Simulation and Bisimulation in Labelled Markov Processes
, 2003
"... This paper presents a fundamental study of similarity and bisimilarity for labelled Markov processes: a particular class of probabilistic labelled transition systems. The main results characterize similarity as a testing preorder and bisimilarity as a testing equivalence. ..."
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This paper presents a fundamental study of similarity and bisimilarity for labelled Markov processes: a particular class of probabilistic labelled transition systems. The main results characterize similarity as a testing preorder and bisimilarity as a testing equivalence.
Domain Theory, Testing and Simulation for Labelled Markov Processes
"... This paper presents a fundamental study of similarity and bisimilarity for labelled Markov processes. The main results characterize similarity as a testing preorder and bisimilarity as a testing equivalence. In general, labelled Markov processes are not required to satisfy a nitebranching condition ..."
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This paper presents a fundamental study of similarity and bisimilarity for labelled Markov processes. The main results characterize similarity as a testing preorder and bisimilarity as a testing equivalence. In general, labelled Markov processes are not required to satisfy a nitebranching conditionindeed the state space may be a continuum, with the transitions given by arbitrary probability measures. Nevertheless we show that to characterize bisimilarity it suces to use nitelybranching labelled trees as tests. Our results involve an interaction between domain theory and measure theory. One of the main technical contributions is to show that a nal object in a suitable category of labelled Markov processes can be constructed by solving a domain equation D = V(D)Act, where V is the probabilistic powerdomain. Given a labelled Markov process whose state space is an analytic space, bisimilarity arises as the kernel of the unique map to the nal labelled Markov process. We also show that the metric for approximate bisimilarity introduced by Desharnais, Gupta, Jagadeesan and Panangaden generates the Lawson topology on the domain D.
Recursively Defined Metric Spaces without Contraction
"... In this paper we use the theory of accessible categories to find fixed points of endofunctors on the category of 1bounded complete metric spaces and nonexpansive functions. In contrast to previous approaches, we do not assume that the endofunctors are locally contractive, and our results do not dep ..."
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In this paper we use the theory of accessible categories to find fixed points of endofunctors on the category of 1bounded complete metric spaces and nonexpansive functions. In contrast to previous approaches, we do not assume that the endofunctors are locally contractive, and our results do not depend on Banach’s fixedpoint theorem. Our approach is particularly suitable for constructing models of systems that feature quantitative data. For instance, using the Kantorovich metric on probability measures we construct a quantitative model for probabilistic transition systems. The metric in our model can reasonably be seen as measuring the behavioural distance between states of the system; it depends exclusively on the transition probabilities and not on an arbitrary discount factor.
18 pages Abstract An Intrinsic Characterization of Approximate Probabilistic Bisimilarity
, 2003
"... 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 probabil ..."
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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. 1