Testing Probabilistic Distributed Systems

There has been much interest in the testing of systems that have physically distributed interfaces and this has been encouraged by recent trends towards the use of such systems. Most formal work in this area has considered the testing of deterministic systems based on deterministic models. However, distributed systems are usually nondeterministic and often can be seen as probabilistic systems in which required or expected probabilities can be attached to the allowable events. This paper provides a formal testing framework for systems with physically distributed interfaces where nondeterministic decisions among alternatives are probabilistically quantified. It first considers testing from systems where there is a unique type of action. In this setting, a generative interpretation of probabilities is adequate and a formal framework to test these systems is provided. However, the observable events of a system are usually divided into inputs and outputs. In such situations it is necessary to use the reactive interpretation of probabilities.