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Behaviour distances to measure the resemblance of two states in a(nondeterministic) fuzzy transition system have been proposed recently in theliterature. Such a distance, defined as a pseudo-ultrametric over the statespace of the model, provides a quantitative analogue of bisimilarity. In thispaper, we focus on the problem of computing these distances. We first extendthe definition of the pseudo-ultrametric by introducing discount such that thediscounting factor being equal to 1 captures the original definition. We thenprovide polynomial-time algorithms to calculate the behavioural distances, inboth the non-discounted and the discounted setting. The algorithm is stronglypolynomial in the former case. Furthermore, we give a polynomial-time algorithmto compute bisimulation over fuzzy transition systems which captures thedistance being equal to 0.

Polynomial-time Algorithms for Computing Distances of Fuzzy Transition Systems