Testing and Refinement for Nondeterministic and Probabilistic Processes

Transition systems are a basic semantic model for formal description , speciication, and analysis of concurrent and distributed systems. In order to describe and analyze aspects of reliability, such as the likelihood of trace and failure, this model has been extended in various ways to handle probabilistic behavior. To use these models for specii-cation and stepwise development of systems, it is important to develop appropriate reenement preorders. In the paper, we develop reenement preorders based on a framework of testing for a model that represents both nondeterministic and probabilistic choices as independent concepts YL92]. Our main contribution is a notion of reward testing, and a de-notational characterization of a testing preorder, which corresponds to a natural probabilistic extension of the trace model Hoa85].