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Unified formal derivation and automatic verification of three binary-tree traversal non-recursive algorithms

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Abstract

Binary tree traversal algorithm can be applied in many aspects, such as information encryption, Network, operating systems, cluster computing and so on. We have already proposed a useful method to verify the correctness of algorithmic programs based on Isabelle proof assistant and Dijkstra’s weakness precondition theory, and have manually derived and verified binary tree traversal non-recursive algorithms in our previous work. In order to ensure the security of the non-recursive algorithms, the focus of this paper is to construct a unified recurrence-relations expression about preorder, in-order, and post-order binary tree traversal non-recursive algorithms. The recurrence-relations expression make it easier to derive the loop invariants of three algorithms. Meanwhile, we automatically verify the correctness of three kinds of non-recursive algorithms by using a generic proof assistant Isabelle. This work realizes mechanically automatic-verification and overcomes the intricacies and weakness of manual verification, improves the verification efficiency, and ensures the trustworthiness and reliability of the algorithm program.

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Acknowledgments

This work was financially supported in part by the National Nature Science Foundation of China (Grant Nos. 61462041, 61462039, 61472167), the National Natural Science Foundation of Jiangxi Province (Grant No. 20142BAB217023) and the Science and Technology Research Project of Jiangxi Province Educational Department (Grant No. GJJ150349).

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Authors and Affiliations

  1. State International S&T Cooperation Base of Networked Supporting Software, Jiangxi Normal University, Nanchang, 330022, China

    Zhen You & Jinyun Xue

  2. Provincial Key Lab of High-Performance Computing, Jiangxi Normal University, Nanchang, 330022, China

    Zhen You & Jinyun Xue

  3. Computer Information Engineering School, Jiangxi Normal University, Nanchang, 330022, China

    Zhengkang Zuo

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  1. Zhen You
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  2. Jinyun Xue
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  3. Zhengkang Zuo
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Correspondence to Zhen You.

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You, Z., Xue, J. & Zuo, Z. Unified formal derivation and automatic verification of three binary-tree traversal non-recursive algorithms. Cluster Comput 19, 2145–2156 (2016). https://doi.org/10.1007/s10586-016-0663-9

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  • DOI: https://doi.org/10.1007/s10586-016-0663-9

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