Language Emptiness of Continuous-Time Parametric Timed Automata

Parametric timed automata extend the standard timed automata with the possibility to use parameters in the clock guards. In general, if the parameters are real-valued, the problem of language emptiness of such automata is undecidable even for various restricted subclasses. We thus focus on the case where parameters are assumed to be integer-valued, while the time still remains continuous. On the one hand, we show that the problem remains undecidable for parametric timed automata with three clocks and one parameter. On the other hand, for the case with arbitrary many clocks where only one of these clocks is compared with (an arbitrary number of) parameters, we show that the parametric language emptiness is decidable. The undecidability result tightens the bounds of a previous result which assumed six parameters, while the decidability result extends the existing approaches that deal with discrete-time semantics only. To the best of our knowledge, this is the first positive result in the case of continuous-time and unbounded integer parameters, except for the rather simple case of single-clock automata

Ready for testing: ensuring conformance to industrial standards through formal verification

The design of distributed, safety-critical real-time systems is challenging due to their high complexity, the potentially large number of components, and complicated requirements and environment assumptions that stem from international standards. We present a case study that shows that despite those challenges, the automated formal verification of such systems is not only possible, but practicable even in the context of small to medium-sized enterprises. We considered a wireless fire alarm system, regulated by the EN 54 standard. We performed formal requirements engineering, modeling and verification and uncovered severe design flaws that would have prevented its certification. For an improved design, we provided dependable verification results which in particular ensure that certification tests for a relevant regulation standard will be passed. In general we observe that if system tests are specified by generalized test procedures, then verifying that a system will pass any test following those test procedures is a cost-efficient approach to improve the product quality based on formal methods. Based on our experience, we propose an approach useful to integrate the application of formal methods to product development in SME.</p