Testing preorders for probabilistic processes can be characterized by simulations

Transition systems are well-established as a semantic model for distributed systems with preorders that serve as criteria for reene-ment of a more abstract transition system to a more concrete one. To reason about probabilistic phenomena such as failure rates, we need to extend models and methods that have proven successful for non-probabilistic systems to a probabilistic setting. In this paper, we develop a reenement preorder for a probabilistic extension of the transition systems model. The preoder is based on a notion of testing, of testing, where reenement corresponds to an improvement in the \worst-case" behavior of a process. The main of the paper result is that this preorder can be described by a notion of probabilistic simulation, which generalizes the standard simulation preorder for ordinary transition system. To our knowledge, this simulation preorder has not been previously described in the literature, and is strictly weaker than previously proposed simulations for probabilistic transition systems.