Talking quiescence: a rigorous theory that supports parallel composition, action hiding and determinisation
This work addresses foundational issues in formal methods for software testing, particularly in model-based testing theory, but it is incremental as it builds on existing input-output transition systems.
The paper tackles the problem of quiescence in behavioral modeling and testing by introducing quiescent transition systems (QTSs) with explicit quiescent transitions and four rules to capture quiescent behavior, and it results in a theory supporting parallel composition, action hiding, and determinization with proofs that these operations preserve the rules.
The notion of quiescence - the absence of outputs - is vital in both behavioural modelling and testing theory. Although the need for quiescence was already recognised in the 90s, it has only been treated as a second-class citizen thus far. This paper moves quiescence into the foreground and introduces the notion of quiescent transition systems (QTSs): an extension of regular input-output transition systems (IOTSs) in which quiescence is represented explicitly, via quiescent transitions. Four carefully crafted rules on the use of quiescent transitions ensure that our QTSs naturally capture quiescent behaviour. We present the building blocks for a comprehensive theory on QTSs supporting parallel composition, action hiding and determinisation. In particular, we prove that these operations preserve all the aforementioned rules. Additionally, we provide a way to transform existing IOTSs into QTSs, allowing even IOTSs as input that already contain some quiescent transitions. As an important application, we show how our QTS framework simplifies the fundamental model-based testing theory formalised around ioco.