We present a Symmetry-based abstraction refinement algorithm SymAR that is directed towards safety verification of large-scale scenarios with complex dynamical systems. The abstraction maps modes with symmetric dynamics to a single abstract mode and refinements recursively split the modes when safety checks fail. We show how symmetry abstractions can be applied effectively to closed-loop control systems, including non-symmetric deep neural network (DNN) controllers. For such controllers, we transform their inputs and outputs to enforce symmetry and make the closed loop system amenable for abstraction. We implemented SymAR in Python and used it to verify paths with 100s of segments in 2D and 3D scenarios followed by a six dimensional DNN-controlled quadrotor, and also a ground vehicle. Our experiments show significant savings, up to 10x in some cases, in verification time over existing methods.

中文翻译：

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SymAR：用于神经网络控制器验证的加速场景的对称抽象和改进

我们提出了一种基于对称性的抽象优化算法SymAR，该算法针对具有复杂动态系统的大规模场景的安全性验证。抽象将具有对称动态的模式映射到单个抽象模式，并且当安全检查失败时，改进会以递归方式拆分模式。我们展示了对称抽象如何可以有效地应用于闭环控制系统，包括非对称深度神经网络（DNN）控制器。对于此类控制器，我们将其输入和输出转换为强制对称性，并使闭环系统适合抽象。我们在Python中实现了SymAR，并用它来验证2D和3D场景中具有100个段的路径，然后是6维DNN控制的四旋翼飞机，以及地面车辆。我们的实验表明可节省大量资金，