Differential Elimination and Algebraic Invariants of Polynomial Dynamical Systems
Symbolic Computation
2026-04-02 v2 Logic in Computer Science
Algebraic Geometry
Dynamical Systems
Abstract
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.
Keywords
Cite
@article{arxiv.2301.10935,
title = {Differential Elimination and Algebraic Invariants of Polynomial Dynamical Systems},
author = {William Simmons and André Platzer},
journal= {arXiv preprint arXiv:2301.10935},
year = {2026}
}
Comments
Final version accepted for publication in Theoretical Computer Science