Elsevier

Theoretical Computer Science

Volume 331, Issue 1, 15 February 2005, Pages 115-142
Theoretical Computer Science

A behavioural pseudometric for probabilistic transition systems

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Abstract

Discrete notions of behavioural equivalence sit uneasily with semantic models featuring quantitative data, like probabilistic transition systems. In this paper, we present a pseudometric on a class of probabilistic transition systems yielding a quantitative notion of behavioural equivalence. The pseudometric is defined via the terminal coalgebra of a functor based on a metric on the space of Borel probability measures on a metric space. States of a probabilistic transition system have distance 0 if and only if they are probabilistic bisimilar. We also characterize our distance function in terms of a real-valued modal logic.

Keywords

Probabilistic transition system
Pseudometric
Probabilistic bisimilarity
Terminal coalgebra
Real-valued modal logic

Cited by (0)

1

Supported by Natural Sciences and Engineering Research Council of Canada.

2

Supported by the US Office of Naval Research.