Proving total correctness and generating preconditions for loop programs via symbolic-numeric computation methods

doi:10.1007/s11704-014-3150-6

Front. Comput. Sci.

2014, Vol. 8

Issue (2) : 192-202 https://doi.org/10.1007/s11704-014-3150-6

RESEARCH ARTICLE

Proving total correctness and generating preconditions for loop programs via symbolic-numeric computation methods

Wang LIN^1,², Min WU¹(

), Zhengfeng YANG¹, Zhenbing ZENG³

¹. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China
². College of Mathematics and Information Science, Wenzhou University, Zhejiang 325035, China
³. Department of Mathematics, Shanghai University, Shanghai 200444, China

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Abstract

We present a symbolic-numeric hybrid method, based on sum-of-squares (SOS) relaxation and rational vector recovery, to compute inequality invariants and ranking functions for proving total correctness and generating preconditions for programs. The SOS relaxation method is used to compute approximate invariants and approximate ranking functions with floating point coefficients. Then Gauss-Newton refinement and rational vector recovery are applied to approximate polynomials to obtain candidate polynomials with rational coefficients, which exactly satisfy the conditions of invariants and ranking functions. In the end, several examples are given to show the effectiveness of our method.

Keywords symbolic computation sum-of-squares relaxation semidefinite programming total correctness precondition generation

Corresponding Author(s): Min WU

Issue Date: 24 June 2014

Cite this article:

Wang LIN,Min WU,Zhengfeng YANG, et al. Proving total correctness and generating preconditions for loop programs via symbolic-numeric computation methods[J]. Front. Comput. Sci., 2014, 8(2): 192-202.

URL:

https://academic.hep.com.cn/fcs/EN/10.1007/s11704-014-3150-6
https://academic.hep.com.cn/fcs/EN/Y2014/V8/I2/192

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