Implementation relations and testing for cyclic systems: Adding probabilities

This paper concerns the systematic testing of robotic control software based on state-based models. We focus cyclic systems that typically receive inputs (values from sensors), perform computations, produce outputs (sent to actuators) and possibly change state. provide a theory for such where time can be represented probabilities are used quantify non-deterministic choices, making it possible model probabilistic algorithms. In addition, refusals, inability system set actions, taken into account. consider several scenarios. For example, tester might only able passively observe sequence events so cannot check probabilities, while in another scenario repeatedly apply test case estimate sequences events. These different scenarios lead range implementation relations (notions correctness). As consequence, this provides formal definitions form basis sound automated also validate by showing how observers an alternative but equivalent characterisation.