Compositional Liveness-Preserving Conformance Testing of Timed I/O Automata -- Technical Report
This work provides a more robust and practical framework for conformance testing in real-time systems, which is incremental but addresses specific limitations in prior theories.
The paper introduces live timed ioco (ltioco), an improved conformance testing theory for timed I/O automata that addresses weaknesses in existing definitions by distinguishing safe and live outputs to handle quiescence in real-time behaviors, and extends zone graphs to enable testing on a finite semantic model, making it feasible for practical tools.
I/O conformance testing theories (e.g., ioco) are concerned with formally defining when observable output behaviors of an implementation conform to those permitted by a specification. Thereupon, several real-time extensions of ioco, usually called tioco, have been proposed, further taking into account permitted delays between actions. In this paper, we propose an improved version of tioco, called live timed ioco (ltioco), tackling various weaknesses of existing definitions. Here, a reasonable adaptation of quiescence (i.e., observable absence of any outputs) to real-time behaviors has to be done with care: ltioco therefore distinguishes safe outputs being allowed to happen, from live outputs being enforced to happen within a certain time period thus inducing two different facets of quiescence. Furthermore, tioco is frequently defined on Timed I/O Labeled Transition Systems (TIOLTS), a semantic model of Timed I/O Automata (TIOA) which is infinitely branching and thus infeasible for practical testing tools. Instead, we extend the theory of zone graphs to enable ltioco testing on a finite semantic model of TIOA. Finally, we investigate compositionality of ltioco with respect to parallel composition including a proper treatment of silent transitions.