Probabilistic testing of asynchronously communicating systems

Input-output labelled transition system (IOLTS) is a state-based model that is widely used to describe the functional behaviour of a reactive system. However when the same system is observed asynchronously through a pair of unbounded FIFO queues (or channels), its apparent behaviour is different from its actual behaviour. This is because an execution trace of the system could appear distorted in a multitude of ways. The apparent behaviour is called the asynchronous behaviour of the system. It is well known that the asynchronous behaviour can also be described by an infinite-state IOLTS. This description however proves to be appropriate only as long as the channels are assumed to be reliable. The moment we throw in unreliability assumptions, the asynchronous behaviour becomes probabilistic in nature. The plain IOLTS model is simply not expressive enough to capture this probabilistic behaviour. To this end, we in this paper show how the asynchronous behaviour of a reactive system can be captured by Segala's probabilistic automata (SPA). We further show how the SPA expressing the asynchronous behaviour can serve as a reference model for probabilistic testing of asynchronously communicating systems.