Formal Methods in System Design

, Volume 46, Issue 2, pp 105–134 | Cite as

Hybrid automata-based CEGAR for rectangular hybrid systems

  • Pavithra PrabhakarEmail author
  • Parasara Sridhar Duggirala
  • Sayan Mitra
  • Mahesh Viswanathan


In this paper, we present a counterexample guided abstraction refinement (CEGAR) framework for systems modelled as rectangular hybrid automata. The main difference, between our approach and previous proposals for CEGAR for hybrid automata, is that we consider the abstractions to be hybrid automata as well, as opposed to finite state systems. We show that the CEGAR scheme is semi-complete for the class of rectangular hybrid automata and complete for the subclass of initialized rectangular automata. We have implemented the CEGAR based algorithm in a tool called Hare, that makes calls to HyTech to analyze the abstract models and validate the counterexamples. The experimental evaluations demonstrate the merits of the approach.


Hybrid system Safety verification Abstraction refinement Counter-example guided abstraction refinement Rectangular hybrid automata 


  1. 1.
    Clarke EM, Grumberg O, Jha S, Lu Y, Veith H (2000) Counterexample-guided abstraction refinement. In: Proceedings of the 12th international conference on computer aided verification, vol 1855 of Lecture Notes in Computer Science. pp 154–169Google Scholar
  2. 2.
    Ball T, Rajamani S (2000) Bebop: a symbolic model checker for Boolean programs. In: Proceedings of the 7th international SPIN, pp 113–130Google Scholar
  3. 3.
    Corbett J, Dwyer M, Hatcliff J, Laubach S, Robby C. Pasareanu, Zheng H (2000) Bandera: extracting finite-state models from Java source code. In: Proceedings of ICSE. pp 439–448Google Scholar
  4. 4.
    Henzinger TA, Jhala R, Majumdar R, Sutre G (2002) Lazy Abstraction. In: Proceedings of 29th ACM symposium on principles of programming languages (POPL’02). pp 58–70Google Scholar
  5. 5.
    Holzmann G, Smith M (2000) Automating software feature verification. Bell Labs Tech J 5(2):72–87CrossRefGoogle Scholar
  6. 6.
    Alur R, Dang T, Ivancic F (2003) Counter-example guided predicate abstraction of hybrid systems. In: Proceedings of TACAS 2003. pp 208–223Google Scholar
  7. 7.
    Clarke EM, Fehnker A, Han Z, Krogh B, Ouaknine J, Stursberg O, Theobald M (2003) Abstraction and counterexample-guided refinement in model checking of hybrid systems. JFCS 14(4):583–604zbMATHMathSciNetGoogle Scholar
  8. 8.
    Clarke E.M., Fehnker A, Han Z, Krogh B, Ouaknine J, Stursberg O, Theobald M (2003) Verification of hybrid systems based on counterexmple-guided abstraction refinement. In: Proceedings of TACAS. pp 192–207Google Scholar
  9. 9.
    Dierks H, Kupferschmid S, Larsen KG (2007) Automatic Abstraction refinement for timed automata. In: Proceedings of FORMATS. pp 114–129Google Scholar
  10. 10.
    Fehnker A, Clarke EM, Jha S, Krogh B (2005) Refining abstractions of hybrid systems using counterexample fragments. In: Proceedings of HSCC 2005. pp 242–257Google Scholar
  11. 11.
    Segelken M (2007) Abstraction and Counterexample-guided construction of omega-automata for model checking of step-discrete linear hybrid models. In: Proceedings of CAV. pp 433–448Google Scholar
  12. 12.
    Sorea M (2004) Lazy approximation for dense real-time systems. In: Proceedings of FORMATS/FTRFTS. pp 363–378Google Scholar
  13. 13.
    Ratschan S, She Z (2007) Safety verification of hybrid systems by constraint propagation based abstraction refinement. ACM Trans Embed Comput Syst 6(1):8Google Scholar
  14. 14.
    Graf S, Saidi H (1997) Construction of abstact state graphs with PVS. In: Proceedings of CAV, pp 72–83Google Scholar
  15. 15.
    Jha SK, Krogh BH, Weimer JE, Clarke EM (2007) Reachability for linear hybrid automata using iterative relaxation abstraction. In: Proceedings of HSCC 2007, pp 287–300Google Scholar
  16. 16.
    Henzinger TA (1996) The theory of hybrid automata. In: LICS, pp 278–292Google Scholar
  17. 17.
    Hybrid abstraction refinement engine (HARE) (2013). In:
  18. 18.
    Henzinger TA, Ho P-H, Howard W-T (1997) Hytech: a model checker for hybrid systems. In: Proceedings of CAV. pp 460–483Google Scholar
  19. 19.
    Frehse G (2005) Phaver: algorithmic verification of hybrid systems past hytech. In: Proceedings of HSCC. pp 258–273Google Scholar
  20. 20.
    Frehse G, Le Guernic C, Donzé A, Cotton S, Ray R, Lebeltel O, Ripado R, Girard A, Dang T, Maler O (2011) SpaceEx: scalable verification of hybrid systems. In Proceedings of CAVGoogle Scholar
  21. 21.
    Asarin E, Dang T, Maler O (2002) The d/dt tool for verification of hybrid systemGoogle Scholar
  22. 22.
    Prabhakar P, Duggirala PS, Mitra S, Viswanathan M (2013) Hybrid automata-based cegar for rectangular hybrid systems. In: Proceedings of VMCAI. pp 48–67Google Scholar
  23. 23.
    Doyen L, Henzinger TA, Raskin J-F (2005) Automatic rectangular refinement of affine hybrid systems. In: Proceedings of FORMATS05, vol 3829 in LNCS. pp 144–161Google Scholar
  24. 24.
    Henzinger TA, Kopke PW, Puri A, Varaiya P (1995) What’s decidable about hybrid automata? In: Proceedings of STOC. pp 373–382Google Scholar
  25. 25.
    Alur Rajeev, Courcoubetis Costas, Halbwachs Nicolas, Henzinger Thomas A, Ho P-H, Nicollin Xavier, Olivero Alfredo, Sifakis Joseph, Yovine Sergio (1995) The algorithmic analysis of hybrid systems. TCS 138(1):3–34CrossRefzbMATHGoogle Scholar
  26. 26.
    Fehnker A, Ivancic F (2004) Benchmarks for hybrid systems verification. pp 326–341Google Scholar
  27. 27.
    Munoz CA, Dowek G, Carreo V (2004) Modeling and verification of an air traffic concept of operations. In: ISSTA, pp 175–182Google Scholar
  28. 28.
    Dutertre B, Sorea M (2004) Timed systems in SAL. Technical report, Computer Science LaboratoryGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Pavithra Prabhakar
    • 1
    Email author
  • Parasara Sridhar Duggirala
    • 2
  • Sayan Mitra
    • 2
  • Mahesh Viswanathan
    • 2
  1. 1.IMDEA Software InstituteMadridSpain
  2. 2.University of Illinois at Urbana-ChampaignChampaignUSA

Personalised recommendations