LOTOS extended with probabilistic behaviours

A common characteristic of process algebras is that they permit us the partial description of concurrent systems by including non-deterministic behaviours. These non-deterministic components are abstractions of the actual ones, and they can be detailed in successive refinements. This paper proposes an enrichment of the above abstraction. It defines a formal description technique which is able to characterize the non-determinism in a probabilistic way. The proposed technique, called LOTOS-P is an upward compatible extension of LOTOS. The compatibility includes also the possibility of specifying non-deterministic behaviours; that is, without probabilistic characterization.The contents of the paper are mainly related to the definition of probabilistic models based on process algebras, and the study of the observable behaviour of systems by using testing relations. The advantage of the proposed model with respect to previous works is twofold. First, the model is simpler, and second, the compatibility with LOTOS is achieved. The simplicity does not make the model useless because its expressive power permits us to express random behaviours in the same way they are being expressed with classical techniques of discrete systems modeling.The probabilistic evaluation of the properties of the system can be done by applying the defined calculus, but also bysimulation. Simulation means that we are able to obtain the desired results with a given confidence level.