A Testing Theory for Real-Time Systems

We develop a testing theory for real-time systems. We keep the usual notion of success or failure (based on finite runs) but we also provide a mechanism of determining the success or failure of infinite runs, using a formalism similar to the acceptance in Büchi automata. We present two refinement timed preorders similar to De Nicola and Hennessy’s may and must testing. We then provide alternative, behavioural and languagebased characterizations for these relations to show that the new preorders are extensions of the traditional preorders. Finally we focus on test generation, showing how tests can be automatically generated out of a timed variant of linear-time logic formulae (namely, TPTL), so that a process must pass the generated test if and only if the process satisfies the given temporal logic formula. Beside the obvious use of such an algorithm (to generate tests), our result also establishes a correspondence between timed must testing and timed temporal logic.