Abstract
In this paper, we investigate how symmetry transformations of equivariant dynamical systems can reduce the computation effort for safety verification. Symmetry transformations of equivariant systems map solutions to other solutions. We build upon this result, producing reachsets from other previously computed reachsets. We augment the standard simulation-based verification algorithm with a new procedure that attempts to verify the safety of the system starting from a new initial set of states by transforming previously computed reachsets. This new algorithm required the creation of a new cache-tree data structure for multi-resolution reachtubes. Our implementation has been tested on several benchmarks and has achieved significant improvements in verification time.
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Acknowledgments
The authors are supported by a research grant from The Boeing Company and a research grant from NSF (CPS 1739966). We would like to thank John L. Olson and Arthur S. Younger from The Boeing Company for valuable technical discussions.
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Sibai, H., Mokhlesi, N., Mitra, S. (2019). Using Symmetry Transformations in Equivariant Dynamical Systems for Their Safety Verification. In: Chen, YF., Cheng, CH., Esparza, J. (eds) Automated Technology for Verification and Analysis. ATVA 2019. Lecture Notes in Computer Science(), vol 11781. Springer, Cham. https://doi.org/10.1007/978-3-030-31784-3_6
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DOI: https://doi.org/10.1007/978-3-030-31784-3_6
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