A Behavioural Pseudometric based on λ–Bisimilarity

In order to describe approximate equivalence among processes, the notions of λ–bisimilarity and behavioural pseudometric have been introduced by Ying and van Breugel respectively. Van Breugel provides a distance function induced by λ–bisimilarity, and conjectures that his behavioural pseudometric coincides with this function. This paper is inspired by this conjecture. We give a negative answer for van Breugel's conjecture first. Moreover, we show that the distance function induced by λ–bisimilarity is a pseudometric on states, and provide a fixed point characterization of this pseudometric.