Talking quiescence: a rigorous theory that supports parallel composition, action hiding and determinisation

TL;DR

This paper introduces quiescent transition systems (QTSs), explicitly modeling quiescence, and develops a comprehensive theory supporting their composition, hiding, and determinisation, thereby enhancing model-based testing frameworks.

Contribution

It formalizes QTSs with rules ensuring accurate quiescent behavior and extends existing IOTSs into QTSs, improving the theoretical foundation for testing and system modeling.

Findings

QTSs explicitly represent quiescence with transitions.

Operations like parallel composition, hiding, and determinisation preserve quiescent rules.

Framework simplifies model-based testing formalism around ioco.

Abstract

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.