Symbolic model checking for discrete real-time systems

  • Xiangyu Luo
  • Lijun Wu
  • Qingliang Chen
  • Haibo Li
  • Lixiao Zheng
  • Zuxi Chen
Research Paper


A considerably large class of critical applications run in distributed and real-time environments, and most of the correctness requirements of such applications must be expressed by time-critical properties. To enable the specification and verification of these properties in both qualitative and quantitative manners, we propose a new real-time temporal logic RTCTL*, by incorporating both the quantitative (bounded) future and past temporal operators from the qualitative temporal logic CTL*. First, we propose a symbolic method for constructing the temporal tester for arbitrary principally temporal formulas. A temporal tester is constructed as a non-deterministic transducer with a fresh boolean output variable, such that at any position the output variable is set to be true if and only if the corresponding formula holds starting from that position. Then we propose a symbolic model checking method for RTCTL* over finite-state transition systems with weak fairness constraints based on the compositionality of testers. The soundness and completeness of the model checking method, the expressiveness of RTCTL*, and the complexity of the tester construction are described and proven. We have already implemented an efficient model checking prototype for the real-time linear temporal logic RTLTL, which is a quantifier-free version of RTCTL*, by building upon the NuSMV model checker. The theoretical and the experimental results from the prototype both confirm that for checking bounded temporal formulae of the form fU[0,b] g or fS[0,b] g, our method performs exponentially better than the translation-based method in NuSMV.


symbolic model checking temporal tester real-time temporal logic just discrete system OBDDs 



This work was supported by National Natural Science Foundation of China (Grant Nos. 61170028, 61572234, 61370072, 71571056), Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 61502184), Program for New Century Excellent Talents in Fujian Province Universities (Grant No. 2013FJ-NCET-ZR03), Natural Foundation Key Program for Young Scholars in the Universities of Fujian Province (Grant No. JZ160409), Natural Science Foundation of Fujian Province (Grant No. 2015J01255), Promotion Program for Young andMiddle-aged Teacher in Science and Technology Research of Huaqiao University (Grant No. ZQN-YX109), and Guangxi Key Laboratory of Trusted Software (Grant No. kx201323).


  1. 1.
    Clarke E M, Grumberg O, Peled D A. Model Checking. London: The MIT Press, 2000Google Scholar
  2. 2.
    Goranko V, Galton A. Temporal logic. In: The Stanford Encyclopedia of Philosophy. San Francisco: Metaphysics Research Lab, Stanford University, 2015Google Scholar
  3. 3.
    Holzmann G J. The SPIN Model Checker-Primer and Reference Manual. Boston: Addison-Wesley, 2004Google Scholar
  4. 4.
    Cimatti A, Clarke E M, Giunchiglia E, et al. Nusmv 2: an opensource tool for symbolic model checking. In: Proceedings of the 14th International Conference on Computer Aided Verification (CAV 2002). Berlin: Springer, 2002. 359–364Google Scholar
  5. 5.
    McMillan K L. Symbolic Model Checking. Norwell: Kluwer Academic Publisher, 1993CrossRefzbMATHGoogle Scholar
  6. 6.
    Pnueli A, Sa’ar Y, Zuck L D. Jtlv: a framework for developing verification algorithms. In: Proceedings of the 22th International Conference on Computer Aided Verification (CAV 2010). Berlin: Springer, 2010. 171–174Google Scholar
  7. 7.
    Su K L, Sattar A, Luo X Y. Model checking temporal logics of knowledge via OBDDs. Comput J, 2007, 50: 403–420CrossRefGoogle Scholar
  8. 8.
    Larsen K G, Pettersson P, Wang Y. UPPAAL in a nutshell. Int J Softw Tools Tech Transfer, 1997, 1: 134–152CrossRefzbMATHGoogle Scholar
  9. 9.
    Henzinger T A, Ho P-H, Howard W-T. HYTECH: a model checker for hybrid systems. Int J Softw Tools Tech Transfer, 1997, 1: 110–122CrossRefzbMATHGoogle Scholar
  10. 10.
    Bozga M, Daws C, Maler O, et al. Kronos: a model-checking tool for real-time systems. In: Proceedings of the 10th International Conference on Computer Aided Verification (CAV 1998). London: Springer-Verlag, 1998. 546–550Google Scholar
  11. 11.
    Georges M, Christoph S. Fully symbolic TCTL model checking for complete and incomplete real-time systems. Sci Comput Program, 2015, 111: 248–276CrossRefGoogle Scholar
  12. 12.
    Alur R, Courcoubetis C, Dill D. Model-checking in dense real-time. Inf Comput, 1993, 104: 2–34MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Alur R, Henzinger T A. Real-time logics: complexity and expressiveness. Inf Comput, 1993, 104: 35–77MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Alur R, Henzinger T A. A really temporal logic. J ACM, 1994, 41: 181–204MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Alur R, Feder T, Henzinger T A. The benefits of relaxing punctuality. J ACM, 1996, 43: 116–146MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Aceto L, Laroussinie F. Is your model checker on time? On the complexity of model checking for timed modal logics. J Log Algebr Program, 2002, 52: 7–51MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Bouyer P, Fahrenberg U, Larsen K G, et al. Model checking real-time systems. In: Handbook of Model Checking. Berlin: Springer-Verlag, 2017Google Scholar
  18. 18.
    Lomuscio A, Qu H Y, Raimondi F. MCMAS: an open-source model checker for the verification of multi-agent systems. Int J Softw Tools Tech Transfer, 2017, 19: 9–30CrossRefGoogle Scholar
  19. 19.
    Bryant R E. Symbolic Boolean manipulation with ordered binary-decision diagrams. ACM Comput Surv, 1992, 24: 293–318CrossRefGoogle Scholar
  20. 20.
    Emerson E A, Mok A K, Sistla A P, et al. Quantitative temporal reasoning. Real-Time Syst, 1992, 4: 331–352CrossRefzbMATHGoogle Scholar
  21. 21.
    Fruth M. Formal verification of embedded real-time systems. Dissertation for Ph.D. Degree. Dresden: TU Dresden, 2005Google Scholar
  22. 22.
    Pnueli A, Zaks A. On the merits of temporal testers. In: 25 Years of Model Checking: History, Achievements, Perspectives. Berlin: Springer, 2008. 172–195CrossRefGoogle Scholar
  23. 23.
    Finkbeiner B, Rabe M N, S´anchez C. Algorithms for model checking HyperLTL and HyperCTL*. In: Proceedings of the 27th International Conference on Computer Aided Verification (CAV 2015). Berlin: Springer, 2015. 30–48Google Scholar
  24. 24.
    Cimatti A, Griggio A, Mover S, et al. Verifying LTL properties of hybrid systems with k-liveness. In: Proceedings of the 27th International Conference on Computer Aided Verification (CAV 2014). Berlin: Springer, 2014. 424–440Google Scholar
  25. 25.
    Cook B, Khlaaf H, Piterman N. On automation of CTL* verification for infinite-state systems. In: Proceedings of the 27th International Conference on Computer Aided Verification (CAV 2015). Berlin: Springer, 2015. 13–29.Google Scholar
  26. 26.
    Zhang N, Duan Z H, Tian C. Model checking concurrent systems with MSVL. Sci China Inf Sci, 2016, 59: 118101CrossRefGoogle Scholar
  27. 27.
    Immler F. Verified reachability analysis of continuous systems. In: Proceedings of the International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS 2015). Berlin: Springer, 2015. 37–51Google Scholar
  28. 28.
    Lin W, Wu M, Yang Z F, et al. Exact safety verification of hybrid systems using sums-of-squares representation. Sci China Inf Sci, 2014, 57: 052101MathSciNetzbMATHGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Xiangyu Luo
    • 1
    • 2
  • Lijun Wu
    • 3
  • Qingliang Chen
    • 4
  • Haibo Li
    • 1
  • Lixiao Zheng
    • 1
  • Zuxi Chen
    • 1
  1. 1.College of Computer Science & TechnologyHuaqiao UniversityXiamenChina
  2. 2.Guangxi Key Laboratory of Trusted SoftwareGuilin University of Electronic TechnologyGuilinChina
  3. 3.School of Computer Science and EngineeringUniversity of Electronic Science and Technology of ChinaChengduChina
  4. 4.Department of Computer ScienceJinan UniversityGuangzhouChina

Personalised recommendations