C2E2: A Verification Tool for Stateflow Models

  • Parasara Sridhar DuggiralaEmail author
  • Sayan Mitra
  • Mahesh Viswanathan
  • Matthew Potok
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9035)


Mathworks’ Stateflow is a predominant environment for modeling embedded and cyber-physical systems where control software interacts with physical processes. We present Compare-Execute-Check-Engine (C2E2)—a verification tool for continuous and hybrid Stateflow models. It checks bounded time invariant properties of models with nonlinear dynamics, and discrete transitions with guards and resets. C2E2 transforms the model, generates simulations using a validated numerical solver, and then computes reachtube over-approximations with increasing precision. For this last step it uses annotations that have to be added to the model. These annotations are extensions of proof certificates studied in Control Theory and can be automatically obtained for linear dynamics. The C2E2 algorithm is sound and it is guaranteed to terminate if the system is robustly safe (or unsafe) with respect to perturbations of guards and invariants of the model. We present the architecture of C2E2, its workflow, and examples illustrating its potential role in model-based design, verification, and validation.


Hybrid System Discrepancy Function Inverted Pendulum Ordinary Differential Equation Reachable State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Angeli, D.: A lyapunov approach to incremental stability properties. IEEE Transactions on Automatic Control (2000)Google Scholar
  2. 2.
    Asarin, E., Dang, T., Maler, O.: The d/dt tool for verification of hybrid systems. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 365–370. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Balluchi, A., Casagrande, A., Collins, P., Ferrari, A., Villa, T., Sangiovanni-Vincentelli, A.: Ariadne: a framework for reachability analysis of hybrid automata. In: International Symposium on Mathematical Theory of Networks and Systems, MNTS (2006)Google Scholar
  4. 4.
    CAPD. Computer assisted proofs in dynamic groups,
  5. 5.
    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)CrossRefGoogle Scholar
  6. 6.
    Deng, Y., Rajhans, A., Julius, A.A.: STRONG: A trajectory-based verification toolbox for hybrid systems. In: Joshi, K., Siegle, M., Stoelinga, M., D’Argenio, P.R. (eds.) QEST 2013. LNCS, vol. 8054, pp. 165–168. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  7. 7.
    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)CrossRefGoogle Scholar
  8. 8.
    Duggirala, P.S., Mitra, S., Viswanathan, M.: Verification of annotated models from executions. In: International Conference on Embedded Software, EMSOFT (2013)Google Scholar
  9. 9.
    Duggirala, P.S., Wang, L., Mitra, S., Viswanathan, M., Muñoz, C.: Temporal precedence checking for switched models and its application to a parallel landing protocol. In: Jones, C., Pihlajasaari, P., Sun, J. (eds.) FM 2014. LNCS, vol. 8442, pp. 215–229. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    Henzinger, T.A., Ho, P.-H., Wong-Toi, H.: HyTech: A model checker for hybrid systems. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 460–463. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  12. 12.
    Huang, Z., Fan, C., Mereacre, A., Mitra, S., Kwiatkowska, M.: Invariant verification of nonlinear hybrid automata networks of cardiac cells. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 373–390. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  13. 13.
    Huang, Z., Mitra, S.: Proofs from simulations and modular annotations. In: International Conference on Hybrid Systems: Computation and Control, pp. 183–192 (2014)Google Scholar
  14. 14.
    Kaynar, D.K., Lynch, N., Segala, R., Vaandrager, F.: The Theory of Timed I/O Automata. Synthesis Lectures on Computer Science. Morgan Kaufmann (November 2005)Google Scholar
  15. 15.
    Larsen, K.G., Pettersson, P., Yi, W.: Uppaal in a nutshell. International Journal on Software Tools for Technology Transfer (STTT) 1(1), 134–152 (1997)CrossRefzbMATHGoogle Scholar
  16. 16.
    Lohmiller, W., Slotine, J.J.E.: On contraction analysis for non-linear systems. Automatica (1998)Google Scholar
  17. 17.
    Manamcheri, K., Mitra, S., Bak, S., Caccamo, M.: A step towards verification and synthesis from simulink/stateflow models. In: International Conference on Hybrid Systems: Computation and Control, HSCC (2011)Google Scholar
  18. 18.
    Nedialkov, N.: VNODE-LP: Validated solutions for initial value problem for ODEs. Technical report, Department of Computing and Software, McMaster University (2006)Google Scholar
  19. 19.
    Nghiem, T., Sankaranarayanan, S., Fainekos, G., Ivancic, F., Gupta, A., Pappas, G.: Monte-carlo techniques for falsification of temporal properties of non-linear hybrid systems. In: International Conference on Hybrid Systems: Computation and Control HSCC (2010)Google Scholar
  20. 20.
    Zou, L., Zhan, N., Wang, S., Franzle, M., Qin, S.: Verifying simulink diagrams via a hybrid hoare logic prover. In: International Conference on Embedded Software EMSOFT (2013)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Parasara Sridhar Duggirala
    • 1
    Email author
  • Sayan Mitra
    • 2
  • Mahesh Viswanathan
    • 1
  • Matthew Potok
    • 2
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana ChampaignChampaignUSA
  2. 2.Department of Electrical and Computer EngineeringUniversity of Illinois at Urbana ChampaignChampaignUSA

Personalised recommendations