Skip to main content
SpringerLink
Log in

Loop reduction techniques for reachability analysis of linear hybrid automata

  • Research Paper
  • Progress of Projects Supported by NSFC
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

The problem of reachability analysis of linear hybrid automata (LHA) is very difficult. This paper considers to improve the efficiency of the reachability analysis by optimizing the structures of LHA. We identify two types of loops called the flexible loops and the zero loops, and present the techniques to replace the repetitions of those loops in the behavior of LHA with finite sequences of locations and in the meantime simplify the associated constraints. The techniques work not only for the polyhedral computing based algorithms but also for the bounded model checkers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Henzinger T A. The theory of hybrid automata. In: Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science, New Brunswick, 1996. 278–292

  2. Asarin E, Maler O, Pnueli A. Reachability analysis of dynamical systems having piecewise-constant derivatives. Theor Comput Sci, 1995, 138: 35–65

    Article  MathSciNet  MATH  Google Scholar 

  3. Alur R, Courcoubetis C, Halbwachs N, et al. The algorithmic analysis of hybrid systems. Theor Comput Sci, 1995, 138: 3–34

    Article  MathSciNet  MATH  Google Scholar 

  4. Alur R, Henzinger T A, Ho P H. Automatic symbolic verification of embedded systems. IEEE Trans Softw Eng, 1996, 22: 181–201

    Article  Google Scholar 

  5. Silva B I, Richeson K, Krogh B, et al. Modeling and verification of hybrid dynamical system using checkmate. In: Proceedings of the 4th International Conference on Automation of Mixed Processes: Hybrid Dynamic Systems. Dortmund, 2000. 323–328

  6. Asarin E, Dang T, Maler O. The d/dt tool for verification of hybrid systems. In: Brinksma E, Larsen K, eds. Computer Aided Verification. Lecture Notes in Computer Science, Vol 2404. Berlin: Springer, 2002. 746–770

    Google Scholar 

  7. Henzinger T A, Ho P H, Wong-Toi H. HyTech: A model checker for hybrid systems. Int J Softw Tools Technol Transf, 1997, 1: 110–122

    Article  MATH  Google Scholar 

  8. Frehse G. Phaver: algorithmic verification of hybrid systems past HyTech. Int J Softw Tools Technol Transf, 2008, 10: 263–279

    Article  MathSciNet  Google Scholar 

  9. Asarin E, Dang T, Frehse G, et al. Recent progress in continuous and hybrid reachability analysis. In: IEEE International Symposium on Computer Aided Control System Design. Washington, DC: IEEE, 2006. 1582–1587

    Google Scholar 

  10. Fränzle M, Herde C. HySat: An efficient proof engine for bounded model checking of hybrid systems. Form Methods Syst Des, 2007, 30: 179–198

    Article  MATH  Google Scholar 

  11. Audemard G, Bozzano M, Cimatti A, et al. Verifying industrial hybrid systems with MathSAT. Electron Notes Theor Comput Sci, 2005, 119: 17–32

    Article  Google Scholar 

  12. Bu L, Li Y, Wang L, et al. BACH: Bounded reachability checker for linear hybrid automata. In: 8th International Conference on Formal Methods in Computer Aided Design, Portland, 2008. 65–68

  13. Bu L, Li X. Path-oriented bounded reachability analysis of composed linear hybrid systems. Int J Softw Tools Technol Transf, 2011, 13: 307–317

    Article  Google Scholar 

  14. Henzinger T A, Ho P H, and Wong-Toi H. HyTech: the next generation. In: 16th IEEE Real-Time Systems Symposium. Washington, DC: IEEE, 1995. 56–65

    Chapter  Google Scholar 

  15. Henzinger T A, Horowitz B, Majumdar R, et al. Beyond HyTech: Hybrid systems analysis using interval numerical methods. In: Lynch N, Krogh B, eds. Hybrid Systems: Computation and Control. Lecture Notes in Computer Science, Vol 1790. Berlin: Springer, 2000, 130–144

    Chapter  Google Scholar 

  16. Bagnara R, Ricci E, Zaffanella E, et al. Possibly not closed convex polyhedra and the parma polyhedra library. In: Hermenegildo M and Puebla G, eds. Static Analysis. Lecture Notes in Computer Science, Vol 2477. Berlin: Springer, 2002, 213–229

    Chapter  Google Scholar 

  17. Stursberg O, Krogh H. Efficient representation and computation of reachable sets for hybrid systems. In: Maler O, Pnueli A, eds. Hybrid Systems: Computation and Control. Lecture Notes in Computer Science, Vol 2623. Berlin: Springer, 2003. 482–497

    Chapter  Google Scholar 

  18. Halbwachs N, Proy Y, Raymond P. Verification of linear hybrid systems by means of convex approximations. In: Le Charlier B, ed. Static Analysis. Lecture Notes in Computer Science, Vol 864. Berlin: Springer, 1994. 223–237

    Chapter  Google Scholar 

  19. Henzinger T A, Ho P H. A note on abstract interpretation strategies for hybrid automata. In: Antsaklis P, Kohn W, Nerode A, eds. Hybrid Systems II. Lecture Notes in Computer Science, Vol 999. Berlin: Springer, 1995. 252–264

    Chapter  Google Scholar 

  20. Asarin E, Dang T, Maler O, et al. Approximate reachability analysis of piecewise-linear dynamical systems. In: Lynch N, Krogh B, eds. Hybrid Systems: Computation and Control. Lecture Notes in Computer Science, Vol 1790. Berlin: Springer, 2000. 20–31

    Chapter  Google Scholar 

  21. Chinneck J W, Dravnieks E W. Locating minimal infeasible constraint sets in linear programs. ORSA J Comput, 1991, 3: 157–168

    Article  MATH  Google Scholar 

  22. Kesten Y, Pnueli A, Sifakis J, et al. Decidable integration graphs. Inf Comput, 1999, 150: 209–243

    Article  MathSciNet  MATH  Google Scholar 

  23. Alur R, Courcoubetis C, Henzinger T A. Computing accumulated delays in real-time systems. Form Methods Syst Des, 1997, 11: 137–155

    Article  Google Scholar 

  24. Henzinger T A, Kopke P W, Puri A, et al. What’s decidable about hybrid automata? J Comput Syst Sci, 1998, 57: 94–124

    Article  MathSciNet  MATH  Google Scholar 

  25. Li X, Zhao J, Yu P, et al. Positive loop-closed automata: a decidable class of hybrid systems. J Logic Algebr Program, 2002: 79–108

  26. Damm W, Ihlemann C, Sofronie-Stokkermans V. Decidability and complexity for the verification of safety properties of reasonable linear hybrid automata. In: Proceedings of the 14th International Conference on Hybrid Systems: Computation and Control. New York: ACM, 2011. 73–82

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory for Novel Software Technology, Department of Computer Science and Technology, Nanjing University, Nanjing, 210093, China

    MinXue Pan, You Li, Lei Bu & XuanDong Li

Authors
  1. MinXue Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. You Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lei Bu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. XuanDong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to XuanDong Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pan, M., Li, Y., Bu, L. et al. Loop reduction techniques for reachability analysis of linear hybrid automata. Sci. China Inf. Sci. 55, 2663–2674 (2012). https://doi.org/10.1007/s11432-012-4726-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-012-4726-0

Keywords

Search

Navigation