Abstract
In this paper, we analyze limits of approximation techniques for (non-linear) continuous image computation in model checking hybrid systems. In particular, we show that even a single step of continuous image computation is not semidecidable numerically even for a very restricted class of functions. Moreover, we show that symbolic insight about derivative bounds provides sufficient additional information for approximation refinement model checking. Finally, we prove that purely numerical algorithms can perform continuous image computation with arbitrarily high probability. Using these results, we analyze the prerequisites for a safe operation of the roundabout maneuver in air traffic collision avoidance.
This research was sponsored by a fellowship of the German Academic Exchange Service (DAAD), by the German Research Council (DFG) under grant SFB/TR 14 AVACS, the National Science Foundation under grant nos. CNS-0411152, CCF-0429120, CCR-0121547, and CCR-0098072, the US Army Research Office under grant no. DAAD19-01-1-0485, and the Office of Naval Research under grant no. N00014-01-1-0796. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, government or other entity.
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Platzer, A., Clarke, E.M. (2007). The Image Computation Problem in Hybrid Systems Model Checking. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds) Hybrid Systems: Computation and Control. HSCC 2007. Lecture Notes in Computer Science, vol 4416. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71493-4_37
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DOI: https://doi.org/10.1007/978-3-540-71493-4_37
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