An iterative method for generating loop invariants

Authors:
Shikun Chen;Zhoujun Li;Xiaoyu Song;Mengjun Li
Affiliations:
School of Computer Science, National University of Defense Technology, Changsha, China;School of Computer, BeiHang University, Beijing, China;Dept. of Electrical and Computer Engineering, Portland State University, Portland, OR;School of Computer Science, National University of Defense Technology, Changsha, China
Venue:
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Year:
2011

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Abstract

Automatic derivation of invariants is one of the critical conundrums in the framework of the inductive program verification methodologies. This paper presents a novel and simple approach to generating polynomial equations as loop invariants. Finite difference of expressions and linear equation solving are harnessed. Unlike related work, the generated constraints are linear equalities, which can be solved efficiently. Furthermore, invariants of higher degree can be constructed in terms of those of lower degree. The case studies demonstrate the effectiveness of the approach.