Invariant sets are a key ingredient for verifying safety and other properties of cyber-physical systems that mix discrete and continuous dynamics. We adapt the elimination-theoretic Rosenfeld-Gr\"{o}bner algorithm to systematically obtain algebraic invariants of polynomial dynamical systems without using Gr\"{o}bner bases or quantifier elimination. We identify totally real varieties as an important class for efficient invariance checking.

翻译：不变量集是验证混合离散与连续动力学的信息物理系统安全及其他性质的关键要素。我们改进基于消去理论的Rosenfeld-Gröbner算法，在不依赖Gröbner基或量词消去的情况下，系统性地获取多项式动力系统的代数不变量。我们识别出全实代数簇作为高效不变性验证的重要类别。