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-Gröbner algorithm to systematically obtain algebraic invariants of polynomial dynamical systems without using Gröbner 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-物理系统安全性及其他性质的关键要素。我们改进了基于消元理论的Rosenfeld-Gröbner算法，在不使用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。我们将全实代数簇确定为高效不变量验证的重要类别。