# Generating exact nonlinear ranking functions by symbolic-numeric hybrid method

@article{Shen2013GeneratingEN,
title={Generating exact nonlinear ranking functions by symbolic-numeric hybrid method},
author={Li-Yong Shen and Min Wu and Zhengfeng Yang and Zhenbing Zeng},
journal={Journal of Systems Science and Complexity},
year={2013},
volume={26},
pages={291-301}
}
• Published 2 April 2013
• Computer Science, Mathematics
• Journal of Systems Science and Complexity
This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial assignments. The authors first transform the problem into a parameterized polynomial optimization problem, and obtain a numerical ranking function using polynomial sum-of-squares relaxation via semidefinite programming (SDP). A rational vector recovery algorithm is deployed to recover a rational polynomial from the numerical…

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