Skip to main content
SpringerLink
Log in

A Compositional Approach to the Verification of Hybrid Systems

  • Chapter
  • First Online:
Theory and Practice of Formal Methods

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9660))

Abstract

The increase of complexity in modelling systems and the chances of success when model-checking them tend to be inversely proportional. This mere observation justifies plainly the need to investigate alternative ways for verification. In this paper we present such an alternative which uses a compositional verification rule. The basic idea is to automatically compute local properties and combine them such that together they are strong enough to prove global safety properties of systems. In [2] we showed how such a rule works in the framework of timed systems with a fixed number of components and in [3] how the whole approach can be extended to the parameterised case. The application of the compositional verification rule can be pushed even further with respect to two directions: (1) hybrid and (2) parametric systems. This is the subject of the present paper.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    compass.informatik.rwth-aachen.de.

  2. 2.

    veriware.org.

  3. 3.

    cps-vo.org/group/ARCH.

  4. 4.

    cps-vo.org/group/UnCoVerCPS.

  5. 5.

    We refer to [13] for an approach which reduces the computation to finding a shortest path in a weighted graph built from the zone graph associated of a timed automaton.

  6. 6.

    The restriction consists in only allowing linear constraints on variables and comparisons between indices while disallowing comparisons between variables and indices.

References

  1. Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.-H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theor. Comput. Sci. 138, 3–34 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  2. Aştefănoaei, L., Rayana, S.B., Bensalem, S., Bozga, M., Combaz, J.: Compositional invariant generation for timed systems. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014 (ETAPS). LNCS, vol. 8413, pp. 263–278. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  3. Aştefănoaei, L., Rayana, S.B., Bensalem, S., Bozga, M., Combaz, J.: Compositional verification of parameterised timed systems. In: Havelund, K., Holzmann, G., Joshi, R. (eds.) NFM 2015. LNCS, vol. 9058, pp. 66–81. Springer, Heidelberg (2015)

    Google Scholar 

  4. Bak, S., Bogomolov, S., Johnson, T.T.: HYST: a source transformation and translation tool for hybrid automaton models. In: HSCC (2015)

    Google Scholar 

  5. Bensalem, S., Bozga, M., Sifakis, J., Nguyen, T.-H.: Compositional verification for component-based systems and application. In: Cha, S.S., Choi, J.-Y., Kim, M., Lee, I., Viswanathan, M. (eds.) ATVA 2008. LNCS, vol. 5311, pp. 64–79. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Bogomolov, S., Donzé, A., Frehse, G., Grosu, R., Johnson, T.T., Ladan, H., Podelski, A., Wehrle, M.: Abstraction-based guided search for hybrid systems. In: Bartocci, E., Ramakrishnan, C.R. (eds.) SPIN 2013. LNCS, vol. 7976, pp. 117–134. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  7. Brockschmidt, M., Larraz, D., Oliveras, A., Carbonell, E.R., Rubio, A.: Compositional safety verification with max-smt. In: FMCAD (2015)

    Google Scholar 

  8. Chen, X., Ábrahám, E., Sankaranarayanan, S.: Flow*: An analyzer for non-linear hybrid systems. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 258–263. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  9. Chen, X., Schupp, S., Makhlouf, I.B., Ábrahám, E., Frehse, G., Kowalewski, S.: A benchmark suite for hybrid systems reachability analysis. In: Havelund, K., Holzmann, G., Joshi, R. (eds.) NFM 2015. LNCS, vol. 9058, pp. 408–414. Springer, Heidelberg (2015)

    Google Scholar 

  10. Cimatti, A.: Application of SMT solvers to hybrid system verification. In: FMCAD (2012)

    Google Scholar 

  11. Cimatti, A., Griggio, A., Mover, S., Tonetta, S.: Parameter synthesis with IC3. In: FMCAD (2013)

    Google Scholar 

  12. Cimatti, A., Griggio, A., Mover, S., Tonetta, S.: HyComp: An SMT-based model checker for hybrid systems. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 52–67. Springer, Heidelberg (2015)

    Google Scholar 

  13. Courcoubetis, C., Yannakakis, M.: Minimum and maximum delay problems in real-time systems. Formal Methods Syst. Des. 1, 385–415 (1992)

    Article  MATH  Google Scholar 

  14. Damm, W., Möhlmann, E., Rakow, A.: Component based design of hybrid systems: a case study on concurrency and coupling. In: HSCC (2014)

    Google Scholar 

  15. David, A., Larsen, K.G., Legay, A., Poulsen, D.B.: Statistical model checking of dynamic networks of stochastic hybrid automata. ECEASST 66 (2013)

    Google Scholar 

  16. Donzé, A.: Breach, A toolbox for verification and parameter synthesis of hybrid systems. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 167–170. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  17. Eggers, A., Ramdani, N., Nedialkov, N., Fränzle, M.: Improving SAT modulo ODE for hybrid systems analysis by combining different enclosure methods. In: Barthe, G., Pardo, A., Schneider, G. (eds.) SEFM 2011. LNCS, vol. 7041, pp. 172–187. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  18. Frehse, G.: Compositional Verification of Hybrid Systems using Simulation Relations. Ph.D. thesis, Radboud Universiteit Nijmegen (2005)

    Google Scholar 

  19. Frehse, G., Le Guernic, C., Donzé, A., Cotton, S., Ray, R., Lebeltel, O., Ripado, R., Girard, A., Dang, T., Maler, O.: SpaceEx: Scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  20. Frehse, G., Jha, S.K., Krogh, B.H.: A counterexample-guided approach to parameter synthesis for linear hybrid automata. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 187–200. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  21. Fribourg, L., Kühne, U.: Parametric verification and test coverage for hybrid automata using the inverse method. Int. J. Found. Comput. Sci. 24, 233–249 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  22. Habermehl, P., Iosif, R., Vojnar, T.: What else is decidable about integer arrays? In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 474–489. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  23. Henzinger, T.A.: The theory of hybrid automata. In: LICS (1996)

    Google Scholar 

  24. Henzinger, T.A., Minea, M., Prabhu, V.S.: Assume-guarantee reasoning for hierarchical hybrid systems. In: Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 275–290. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  25. Henzinger, T.A., Wong-Toi, H.: Using HyTech to synthesize control parameters for a steam boiler. In: Abrial, J.-R., Börger, E., Langmaack, H. (eds.) FMIA 1996. LNCS, vol. 1165. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  26. Hermanns, H., Krčál, J., Křetínský, J.: Compositional verification and optimization of interactive markov chains. In: D’Argenio, P.R., Melgratti, H. (eds.) CONCUR 2013 – Concurrency Theory. LNCS, vol. 8052, pp. 364–379. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  27. Ho, P.-H.: Automatic Analysis of Hybrid Systems. Ph.D. thesis, Cornell University (1995)

    Google Scholar 

  28. Jaffe, M.S., Leveson, N.G., Heimdahl, M.P.E., Melhart, B.E.: Software requirements analysis for real-time process-control systems. IEEE Trans. Softw. Eng. 17, 241–258 (1991)

    Article  Google Scholar 

  29. Jeannin, J., Platzer, A.: dtl2: Differential temporal dynamic logic with nested temporalities for hybrid systems. In: IJCAR (2014)

    Google Scholar 

  30. Johnson, T.T., Mitra, S.: A small model theorem for rectangular hybrid automata networks. In: Giese, H., Rosu, G. (eds.) FORTE 2012 and FMOODS 2012. LNCS, vol. 7273, pp. 18–34. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  31. Johnson, T.T., Mitra, S.: Anonymized reachability of hybrid automata networks. In: Legay, A., Bozga, M. (eds.) FORMATS 2014. LNCS, vol. 8711, pp. 130–145. Springer, Heidelberg (2014)

    Google Scholar 

  32. Kong, S., Gao, S., Chen, W., Clarke, E.: \({\sf dReach}\): \(\delta \)-reachability analysis for hybrid systems. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 200–205. Springer, Heidelberg (2015)

    Google Scholar 

  33. Legay, A., Bensalem, S., Boyer, B., Bozga, M.: Incremental generation of linear invariants for component-based systems. In: ACSD (2013)

    Google Scholar 

  34. Lynch, N.A., Segala, R., Vaandrager, F.W.: Hybrid I/O automata. Inf. Comput. 185, 105–157 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  35. de Moura, L., Bjørner, N.S.: Efficient e-matching for SMT solvers. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 183–198. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  36. Mover, S.: Verification of Hybrid Systems using Satisfiability Modulo Theories. Ph.D. thesis, FBK-IRST/DIT (2014)

    Google Scholar 

  37. Mover, S., Cimatti, A., Tiwari, A., Tonetta, S.: Time-aware relational abstractions for hybrid systems. In: EMSOFT (2013)

    Google Scholar 

  38. Oehlerking, J.: Decomposition of Stability Proofs for Hybrid Systems. Ph.D. thesis, Carl von Ossietzky Universität, Oldenburg (2011)

    Google Scholar 

  39. Quesel, J.-D., Platzer, A.: Playing hybrid games with KeYmaera. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 439–453. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  40. Somenzi, F., Bradley, A.R.: IC3: where monolithic and incremental meet. In: FMCAD (2011)

    Google Scholar 

  41. Testylier, R., Dang, T.: NLTOOLBOX: A library for reachability computation of nonlinear dynamical systems. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 469–473. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  42. Zhang, L., She, Z., Ratschan, S., Hermanns, H., Hahn, E.M.: Safety verification for probabilistic hybrid systems. Eur. J. Control 18, 588–590 (2012)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

We would like to thank Chih-Hong Cheng for his friendly feedback and for sharing some ideas about possible ways to tackle decomposition.

Author information

Authors and Affiliations

  1. fortiss - An-Institut TUM, Guerickestr. 25, 80805, München, Germany

    Lăcrămioara Aştefănoaei

  2. UJF-Grenoble, CNRS VERIMAG UMR 5104, 38041, Grenoble, France

    Saddek Bensalem & Marius Bozga

Authors
  1. Lăcrămioara Aştefănoaei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Saddek Bensalem
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marius Bozga
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lăcrămioara Aştefănoaei .

Editor information

Editors and Affiliations

  1. Informatik 2, RWTH Aachen University Informatik 2, Aachen, Germany

    Erika Ábrahám

  2. Leiden University , Leiden, The Netherlands

    Marcello Bonsangue

  3. University of Oslo , Oslo, Norway

    Einar Broch Johnsen

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Aştefănoaei, L., Bensalem, S., Bozga, M. (2016). A Compositional Approach to the Verification of Hybrid Systems. In: Ábrahám, E., Bonsangue, M., Johnsen, E. (eds) Theory and Practice of Formal Methods. Lecture Notes in Computer Science(), vol 9660. Springer, Cham. https://doi.org/10.1007/978-3-319-30734-3_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-30734-3_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30733-6

  • Online ISBN: 978-3-319-30734-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation