Domain theory, testing and simulation for labelled Markov processes

Our results involve an interaction between domain theory and measure theory. One of the main technical contributions is to show that a final object in a suitable category of LMPs can be constructed by solving a domain equation D≅V(D)Act, where V is the probabilistic powerdomain. Given an LMP whose state space is an analytic space, bisimilarity arises as the kernel of the unique map to the final LMP. We also show that the metric for approximate bisimilarity introduced by Desharnais, Gupta, Jagadeesan and Panangaden generates the Lawson topology on the domain D.