A Theory of Testing for Soft Real-Time Processes

We present a semantic framework for soft real-time processes, i.e., processes that meet their deadlines most of the time. The key components of our framework are: (1) a speciication language PDP (for Probabilistic and Discrete-time Processes) that incorporates both prob-abilistic and timing aspects of process behavior; (2) a formal operational semantics for PDP given as a re-cursively deened probability distribution function over process terms and atomic actions; and (3) a natural notion of a process passing a test with a certain probability , where a test is a process with the added capability of reporting success. By encoding deadlines as tests, the probability of a process passing a test may now be interpreted as the probability of the process meeting a deadline, thereby capturing the essence of soft real-time. A simple video frame transmission example illustrates our approach.