Generating exact nonlinear ranking functions by symbolic-numeric hybrid method

  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},
  • L. Shen, Min Wu, Zhenbing Zeng
  • 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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