Approximate Bisimulation Minimisation

We propose polynomial-time algorithms to minimise labelled Markov chains whose transition probabilities are not known exactly, have been perturbed, or can only be obtained by sampling. Our algorithms are based on a new notion of an approximate bisimulation quotient, obtained by lumping together states that are exactly bisimilar in a slightly perturbed system. We present experiments that show that our algorithms are able to recover the structure of the bisimulation quotient of the unperturbed system.