Time for Quiescence: Modelling quiescent behaviour in testing via time-outs in timed automata

2025-07-24

AI Summary

Modeling quiescence in model-based testing (MBT) typically relies on complex timed automata (TA), hindering scalability and practical adoption. Method: This paper proposes a lightweight temporal extension to labeled transition systems (LTS): introducing a single global clock and a user-configurable timeout threshold $M$, together with a formal $chi^M$ lifting operator to construct an equivalent timed automaton. Contribution/Results: The approach formally captures quiescence while preserving LTS simplicity and ensuring strict equivalence between ioco and tioco$_M$ conformance relations. We prove three key properties: (1) semantic conformance equivalence; (2) order independence (commutativity) of test case generation; and (3) consistency of test verdicts. By providing a concise, reliable, and formally verifiable foundation for timeout-based quiescence detection, the method bridges a critical gap between theory and industrial practice in MBT.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Model-based testing (MBT) derives test suites from a behavioural specification of the system under test. In practice, engineers favour simple models, such as labelled transition systems (LTSs). However, to deal with quiescence - the absence of observable output - in practice, a time-out needs to be set to conclude observation of quiescence. Timed MBT exists, but it typically relies on the full arsenal of timed automata (TA). We present a lifting operator $χ^{scriptstyle M}!$ that adds timing without the TA overhead: given an LTS, $χ^{scriptstyle M}!$ introduces a single clock for a user chosen time bound $M>0$ to declare quiescence. In the timed automaton, the clock is used to model that outputs should happen before the clock reaches value $M$, while quiescence occurs exactly at time $M$. This way we provide a formal basis for the industrial practice of choosing a time-out to conclude quiescence. Our contributions are threefold: (1) an implementation conforms under $mathbf{ioco}$ if and only if its lifted version conforms under timed $mathbf{tioco_M}$ (2) applying $χ^{scriptstyle M}!$ before or after the standard $mathbf{ioco}$ test-generation algorithm yields the same set of tests, and (3) the lifted TA test suite and the original LTS test suite deliver identical verdicts for every implementation.

Problem

• Modeling quiescent behavior in testing via time-outs
• Simplifying timed model-based testing with LTS and single clock
• Formalizing time-out choice for quiescence in industrial practice

Innovation

• Lifts LTS to timed automata with single clock
• Uses time-bound M to declare quiescence formally
• Ensures ioco and tioco_M conformance equivalence