Model Checking of Mixed Multi-Models Sample Clauses

Model Checking of Mixed Multi-Models. ‌ The nature of multi-models as defined in INTO-CPS is not dissimilar to gen- eral hybrid systems, which can be seen as systems containing both, physical components that evolve over time and discrete components that may influ- ence the continuous dynamics. Despite the substantial effort that was put into the development of hybrid model checking, there are still open questions that need to be answered in order to increase the applicability and usabil- ity of hybrid model checking tools. We therefore deviate from representing multi-models by what they are — hybrid systems — and consider DE ab- stractions of their continuous behaviors, which can be seen as a response to the scalability issues of hybrid model checking. A classical approach to representing hybrid systems is to apply hybrid au- tomata [ACH+95, Hen96], which are a formalism that can accurately de- scribe systems composed of a mixture of discrete and continuous behaviors by expressing the behavior of continuous variables using ordinary differen- tial equations. A textbook example of an execution of a hybrid automaton is given in Fig. 1, depicting the behavior of a bouncing ball dropped from some initial height with zero initial velocity. Due to gravity, the ball initially accelerates towards the ground and falls until it hits the ground. It then bounces back whilst losing some of its kinetic energy, and raise again. Figure 1: Continuous-time behavior of a bouncing ball. There is, of course, a multitude of ways of the continuous behavior of a bounc- ing ball could be represented using a discrete abstraction. In the following, Fig. 2 and Fig. 3 show two abstractions used in the INTO-CPS Applica- tion [BM15, BLM16]. Figure 2 abstracts the entire state space of y over t using one tight interval that contains all potential values. Figure 3 shows how the hybrid behavior can automatically be abstracted using a sequence of intervals which are based on a concrete simulation, which yields much more precise results. In this approach, time-discretization is applied and one interval is used to capture all values of y within a fixed-size timeframe. Figure 2: Continuous-time behavior of a bouncing ball abstracted via a single interval. Approaches for deriving and handling such interval abstractions have been the topic of previous deliverables [BM15, BLM16]. The focus of this de- liverable is the combination of multi-models for model checking, and the application in the INTO-CPS project. Figure 3: Continuous-time...