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This paper presents a fundamental study of similarity and bisimilarity for labelled Markov processes (LMPs). The main results characterize similarity as a testing preorder and bisimilarity as a testing equivalence. In general, LMPs are not required to satisfy a finite-branching condition-indeed the state space may be a continuum, with the transitions given by arbitrary probability measures. Nevertheless we show that to characterize bisimilarity it suffices to use finitely-branching labelleddoi:10.1016/j.tcs.2004.10.021 fatcat:ej6wdbof75czpcvxi3rjxkvyga