We continue the work of Wong and Wonham on discrete-event observers, by specializing their algorithms for general causal reporter maps to natural projections. Unlike the former, a natural projection does not always admit a unique smallest extension to a natural observer. Instead there may exist several minimal extensions to the original observable event set. We show that the problem of finding such a minimal extension is NP-hard. However, we propose a polynomial-time algorithm that always finds some extension to a natural observer. While this is not guaranteed to be minimal, it is in practice often reasonably small.
Abstract. We present case studies which show how the paradigm of learning-based testing (LBT) can be successfully applied to black-box requirements testing of industrial reactive systems. For this, we apply a new testing tool LBTest, which combines algorithms for incremental black-box learning of Kripke structures with model checking technology. We show how test requirements can be modeled in propositional linear temporal logic extended by finite data types. We then provide benchmark performance results for LBTest applied to three industrial case studies.
Highly automated road vehicles need the capability of stopping safely in a situation that disrupts continued normal operation, e.g. due to internal system faults. Motion planning for safe stop differs from nominal motion planning, since there is not a specific goal location. Rather, the desired behavior is that the vehicle should reach a stopped state, preferably outside of active lanes. Also, the functionality to stop safely needs to be of high integrity. The first contribution of this paper is to formulate the safe stop problem as a benchmark optimal control problem, which can be solved by dynamic programming. However, this solution method cannot be used in real-time. The second contribution is to develop a real-time safe stop trajectory planning algorithm, based on selection from a precomputed set of trajectories. By exploiting the particular properties of the safe stop problem, the cardinality of the set is decreased, making the algorithm computationally efficient. Furthermore, a monitoring based architecture concept is proposed, that ensures dependability of the safe stop function. Finally, a proof of concept simulation using the proposed architecture and the safe stop trajectory planner is presented.
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