Characterization of Simulation by Probabilistic Testing

Testing of systems naturally has a non-deterministic character: on the one hand, internal decisions of the system under test appear as non-determinism to an observer; on the other hand, the system under test inevitably receives inputs from the environment that are not controlled by the tester. To model both aspects, we investigate a probabilistic testing framework in which non-deterministic labelled transition systems are examined through execution of finite, probabilistic test-cases. We show that the simulation preorder on labelled transition systems can be tested probabilistically, elegantly recapturing the notion of conformance testing in this setting.