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A Linear Programming Relaxation Based Approach for Generating Barrier Certificates of Hybrid Systems

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FM 2016: Formal Methods (FM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9995))

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Abstract

This paper presents a linear programming (LP) relaxation based approach for generating polynomial barrier certificates for safety verification of semi-algebraic hybrid systems. The key idea is to introduce an LP relaxation to encode the set of nonnegativity constraints derived from the conditions of the associated barrier certificates and then resort to LP solvers to find the solutions. The most important benefit of the LP relaxation based approach is that it possesses a much lower computational complexity and hence can be solved very efficiently, which is demonstrated by the theoretical analysis on complexity as well as the experiment on a set of examples gathered from the literature. As far as we know, it is the first method that enables LP relaxation based polynomial barrier certificate generation.

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Acknowledgments

This material is supported in part by Key Basic Research Program of China (Grant No. 2014CB340703), the National Natural Science Foundation of China (Grant Nos. 61321064, 61361136002, 11471209, 11571350, 61672435, 61561146394, 91318301 and 61602348), the Innovation Program of Shanghai Municipal Education Commission (Grant No. 14ZZ046), the project on the Integration of Industry, Education and Research of Jiangsu Province (Grant No. BY2014126-03), the project SWU116007 funded by Southwest University. We would like to thank anonymous reviewers for their very valuable comments.

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Authors and Affiliations

  1. Shanghai Key Lab of Trustworthy Computing, East China Normal University, Shanghai, China

    Zhengfeng Yang

  2. State Key Lab for Novel Software Technology, Nanjing University, Nanjing, China

    Chao Huang & Xin Chen

  3. Key Lab of Mathematics Mechanization, AMSS, CAS, Beijing, China

    Wang Lin

  4. Center for Research and Innovation in Software Engineering, Southwest University, Chongqing, China

    Zhiming Liu

Authors
  1. Zhengfeng Yang
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  2. Chao Huang
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  3. Xin Chen
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  4. Wang Lin
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  5. Zhiming Liu
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Corresponding author

Correspondence to Wang Lin .

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Editors and Affiliations

  1. Newcastle University, Newcastle upon Tyne, United Kingdom

    John Fitzgerald

  2. US Naval Research Laboratory, Washington, District of Columbia, USA

    Constance Heitmeyer

  3. ISTI-CNR, Pisa, Italy

    Stefania Gnesi

  4. University of Cyprus, Nicosia, Cyprus

    Anna Philippou

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Yang, Z., Huang, C., Chen, X., Lin, W., Liu, Z. (2016). A Linear Programming Relaxation Based Approach for Generating Barrier Certificates of Hybrid Systems. In: Fitzgerald, J., Heitmeyer, C., Gnesi, S., Philippou, A. (eds) FM 2016: Formal Methods. FM 2016. Lecture Notes in Computer Science(), vol 9995. Springer, Cham. https://doi.org/10.1007/978-3-319-48989-6_44

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  • DOI: https://doi.org/10.1007/978-3-319-48989-6_44

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  • Online ISBN: 978-3-319-48989-6

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