Bisimulation through probabilistic testing
Information and Computation
On the combinatorial and algebraic complexity of quantifier elimination
Journal of the ACM (JACM)
Deciding bisimilarity and similarity for probabilistic processes
Journal of Computer and System Sciences
Bisimulation indexes and their applications
Theoretical Computer Science
The Metric Analogue of Weak Bisimulation for Probabilistic Processes
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Toward an Approximation Theory for Computerised Control
EMSOFT '02 Proceedings of the Second International Conference on Embedded Software
Concurrency and Automata on Infinite Sequences
Proceedings of the 5th GI-Conference on Theoretical Computer Science
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
A probabilistic polynomial-time process calculus for the analysis of cryptographic protocols
Theoretical Computer Science
Approximating and computing behavioural distances in probabilistic transition systems
Theoretical Computer Science
Results on the quantitative μ-calculus qMμ
ACM Transactions on Computational Logic (TOCL)
Metrics for Action-labelled Quantitative Transition Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Discounting the future in systems theory
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
On metrics for probabilistic systems: Definitions and algorithms
Computers & Mathematics with Applications
The Kantorovich Metric in Computer Science: A Brief Survey
Electronic Notes in Theoretical Computer Science (ENTCS)
Continuous time and/or continuous distributions
EPEW'10 Proceedings of the 7th European performance engineering conference on Computer performance engineering
Bisimulation Metrics for Continuous Markov Decision Processes
SIAM Journal on Computing
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Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of behavioural pseudometrics for probabilistic transition systems. These pseudometrics are a quantitative analogue of probabilistic bisimilarity. Distance zero captures probabilistic bisimilarity. Each pseudometric has a discount factor, a real number in the interval (0, 1]. The smaller the discount factor, the more the future is discounted. If the discount factor is one, then the future is not discounted at all. Desharnais et al. showed that the behavioural distances can be calculated up to any desired degree of accuracy if the discount factor is smaller than one. In this paper, we show that the distances can also be approximated if the future is not discounted. A key ingredient of our algorithm is Tarski's decision procedure for the first order theory over real closed fields. By exploiting the Kantorovich-Rubinstein duality theorem we can restrict to the existential fragment for which more efficient decision procedures exist.