Bisimulation through probabilistic testing
Information and Computation
Reactive, generative, and stratified models of probabilistic processes
Information and Computation
Journal of the ACM (JACM)
Communication and Concurrency
The Metric Analogue of Weak Bisimulation for Probabilistic Processes
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Modeling and Verification of Randomized Distributed Real -Time Systems
Modeling and Verification of Randomized Distributed Real -Time Systems
Metrics for labelled Markov processes
Theoretical Computer Science - Logic, semantics and theory of programming
A behavioural pseudometric for probabilistic transition systems
Theoretical Computer Science - Automata, languages and programming
A behavioural pseudometric for metric labelled transition systems
CONCUR 2005 - Concurrency Theory
On Behavioral Metric for Probabilistic Systems: Definition and Approximation Algorithm
FSKD '07 Proceedings of the Fourth International Conference on Fuzzy Systems and Knowledge Discovery - Volume 02
Metrics for Action-labelled Quantitative Transition Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Approximating a behavioural pseudometric without discount for probabilistic systems
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
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In this paper, we consider the behavioral pseudometrics for probabilistic systems, which are a quantitative analogue of probabilistic bisimilarity in the sense that the distance zero captures the probabilistic bisimilarity. The model we are interested in is probabilistic automata, which are based on state transition systems and make a clear distinction between probabilistic and nondeterministic choices. The pseudometrics are defined as the greatest fixpoint of a monotonic functional on the complete lattice of state metrics. A distinguished characteristic of this pseudometric lies in that it does not discount the future, which addresses some algorithmic challenges to compute the distance of two states in the model. We solve this problem by providing an approximation algorithm: up to any desired degree of accuracy @e, the distance can be approximated to within @e in time exponential in the size of the model and logarithmic in 1@e. One of the key ingredients of our algorithm is to express a pseudometric being a post-fixpoint as the elementary sentence over real closed fields, which allows us to exploit Tarski's decision procedure, together with the binary search to approximate the behavioral distance.