Vacuity is a leading sanity check in model-checking, applied when the system is found to satisfy the specification. The check detects situations where the specification passes in a trivial way, say when a specification that requires every request to be followed by a grant is satisfied in a system with no requests. Such situations typically reveal problems in the modelling of the system or the specification, and indeed vacuity detection is a part of most industrial model-checking tools. Existing research and tools for vacuity concern discrete-time systems and specification formalisms. We introduce real-time vacuity, which aims to detect problems with real-time modelling. Real-time logics are used for the specification and verification of systems with a continuous-time behavior. We study vacuity for the branching real-time logic TCTL, and focus on vacuity with respect to the time constraints in the specification. Specifically, the logic TCTL includes the temporal operator UJ, which specifies real-time eventualities in real-time systems: the parameter is an interval with integral boundaries that bounds the time in which the eventuality should hold. We define several tightenings for the UJ operator. These tightenings require the eventuality to hold within a strict subset of J. We prove that vacuity detection for TCTL is PSPACE-complete, thus it does not increase the complexity of model-checking of TCTL. Our contribution involves an extension, termed TCTL +, of TCTL, which allows the interval J not to be continuous, and for which model checking stays in PSPACE. Finally, we describe a method for ranking vacuity results according to their significance.
|Original language||American English|
|Title of host publication||Formal Methods - 22nd International Symposium, FM 2018, Held as Part of the Federated Logic Conference, FloC 2018, Proceedings|
|Editors||Klaus Havelund, Bill Roscoe, Erik de Vink, Jan Peleska|
|Number of pages||18|
|State||Published - 2018|
|Event||22nd International Symposium on Formal Methods, FM 2018 Held as Part of the Federated Logic Conference, FloC 2018 - Oxford, United Kingdom|
Duration: 15 Jul 2018 → 17 Jul 2018
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||22nd International Symposium on Formal Methods, FM 2018 Held as Part of the Federated Logic Conference, FloC 2018|
|Period||15/07/18 → 17/07/18|
Bibliographical notePublisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.