Discrete Event Dynamic Systems

, Volume 27, Issue 2, pp 443–461 | Cite as

Order-reduction abstractions for safety verification of high-dimensional linear systems

  • Hoang-Dung Tran
  • Luan Viet Nguyen
  • Weiming Xiang
  • Taylor T. Johnson


Order-reduction is a standard automated approximation technique for computer-aided design, analysis, and simulation of many classes of systems, from circuits to buildings. To be used as a sound abstraction for formal verification, a measure of the similarity of behavior must be formalized and computed, which we develop in a computational way for a class of asymptotic stable linear systems as the main contributions of this paper. We have implemented the order-reduction as a sound abstraction process through a source-to-source model transformation in the HyST tool and use SpaceEx to compute sets of reachable states to verify properties of the full-order system through analysis of the reduced-order system. Our experimental results suggest systems with thousand of state variables can be reduced to systems with tens of state variables such that the order-reduction overapproximation error is small enough to prove or disprove safety properties of interest using current reachability analysis tools. Our results illustrate this approach is effective in tackling the state-space explosion problem for verification of high-dimensional linear systems.


Abstraction Model reduction Order reduction Verification Reachability analysis 



The authors gratefully acknowledge the detailed feedback provided by the reviewers, which have helped improve this manuscript. The authors thank Dr. Andrew Sogokon of Vanderbilt University for carefully reading and providing feedback on the final draft of the manuscript. The material presented in this paper is based upon work supported by the National Science Foundation (NSF) under grant numbers CNS 1464311 and SHF 1527398, the Air Force Research Laboratory (AFRL) through contract number FA8750-15-1-0105, and the Air Force Office of Scientific Research (AFOSR) under contract numbers FA9550-15-1-0258 and FA9550-16-1-0246. The U.S. government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of AFRL, AFOSR, or NSF.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Hoang-Dung Tran
    • 1
  • Luan Viet Nguyen
    • 2
  • Weiming Xiang
    • 1
  • Taylor T. Johnson
    • 1
  1. 1.Vanderbilt UniversityNashvilleUSA
  2. 2.University of Texas at ArlingtonArlingtonUSA

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