Approximating a Behavioural Pseudometric Without Discount for Probabilistic Systems

  • Franck van Breugel
  • Babita Sharma
  • James Worrell
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4423)


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.


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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Franck van Breugel
    • 1
  • Babita Sharma
    • 1
  • James Worrell
    • 2
  1. 1.York University, 4700 Keele Street, Toronto, M3J 1P3Canada
  2. 2.Oxford University Computing Laboratory, Parks Road, Oxford, OX1 3QDEngland

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