Advertisement

Approximate Partial Order Reduction

  • Chuchu Fan
  • Zhenqi Huang
  • Sayan Mitra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10951)

Abstract

We present a new partial order reduction method for reachability analysis of nondeterministic labeled transition systems over metric spaces. Nondeterminism arises from both the choice of the initial state and the choice of actions, and the number of executions to be explored grows exponentially with their length. We introduce a notion of \(\varepsilon \)-independence relation over actions that relates approximately commutative actions; \(\varepsilon \)-equivalent action sequences are obtained by swapping \(\varepsilon \)-independent consecutive action pairs. Our reachability algorithm generalizes individual executions to cover sets of executions that start from different, but \(\delta \)-close initial states, and follow different, but \(\varepsilon \)-independent, action sequences. The constructed over-approximations can be made arbitrarily precise by reducing the \(\delta ,\varepsilon \) parameters. Exploiting both the continuity of actions and their approximate independence, the algorithm can yield an exponential reduction in the number of executions explored. We illustrate this with experiments on consensus, platooning, and distributed control examples.

References

  1. 1.
    Abdulla, P., Aronis, S., Jonsson, B., Sagonas, K.: Optimal dynamic partial order reduction. In: ACM SIGPLAN Notices, vol. 49, pp. 373–384. ACM (2014)Google Scholar
  2. 2.
    Alur, R., Brayton, R.K., Henzinger, T.A., Qadeer, S., Rajamani, S.K.: Partial-order reduction in symbolic state space exploration. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 340–351. Springer, Heidelberg (1997).  https://doi.org/10.1007/3-540-63166-6_34CrossRefGoogle Scholar
  3. 3.
    Baier, C., Größer, M., Ciesinski, F.: Partial order reduction for probabilistic systems. QEST 4, 230–239 (2004)Google Scholar
  4. 4.
    Baier, C., Katoen, J.P., Larsen, K.G.: Principles of Model Checking. MIT press, Cambridge (2008)zbMATHGoogle Scholar
  5. 5.
    Blondel, V., Hendrickx, J.M., Olshevsky, A., Tsitsiklis, J., et al.: Convergence in multiagent coordination, consensus, and flocking. In: IEEE Conference on Decision and Control, vol. 44, p. 2996. IEEE; 1998 (2005)Google Scholar
  6. 6.
    Cassez, F., Ziegler, F.: Verification of concurrent programs using trace abstraction refinement. In: Davis, M., Fehnker, A., McIver, A., Voronkov, A. (eds.) LPAR 2015. LNCS, vol. 9450, pp. 233–248. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48899-7_17CrossRefGoogle Scholar
  7. 7.
    Chaudhuri, S., Gulwani, S., Lublinerman, R.: Continuity and robustness of programs. Commun. ACM 55(8), 107–115 (2012)CrossRefGoogle Scholar
  8. 8.
    Clarke, E., Jha, S., Marrero, W.: Partial order reductions for security protocol verification. In: Graf, S., Schwartzbach, M. (eds.) TACAS 2000. LNCS, vol. 1785, pp. 503–518. Springer, Heidelberg (2000).  https://doi.org/10.1007/3-540-46419-0_34CrossRefzbMATHGoogle Scholar
  9. 9.
    Clarke, E.M., Grumberg, O., Minea, M., Peled, D.: State space reduction using partial order techniques. Int. J. Softw. Tools Technol. Transfer 2(3), 279–287 (1999)CrossRefGoogle Scholar
  10. 10.
    Clarke, E.M., Grumberg, O., Peled, D.: Model Checking. MIT press, Cambridge (1999)Google Scholar
  11. 11.
    Donzé, A.: Breach, a toolbox for verification and parameter synthesis of hybrid systems. In: Computer Aided Verification (CAV) (2010)CrossRefGoogle Scholar
  12. 12.
    Donzé, A., Maler, O.: Systematic simulation using sensitivity analysis. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 174–189. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-71493-4_16CrossRefGoogle Scholar
  13. 13.
    Duggirala, P.S., Mitra, S., Viswanathan, M.: Verification of annotated models from executions. In: EMSOFT (2013)Google Scholar
  14. 14.
    Duggirala, P.S., Mitra, S., Viswanathan, M., Potok, M.: C2E2: a verification tool for stateflow models. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 68–82. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46681-0_5CrossRefGoogle Scholar
  15. 15.
    Fan, C., Huang, Z., Mitra, S.: Approximate partial order reduction (full version), May 2018. https://arxiv.org/abs/1610.06317
  16. 16.
    Fan, C., Mitra, S.: Bounded verification with on-the-fly discrepancy computation. In: Finkbeiner, B., Pu, G., Zhang, L. (eds.) ATVA 2015. LNCS, vol. 9364, pp. 446–463. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-24953-7_32CrossRefzbMATHGoogle Scholar
  17. 17.
    Fang, L., Antsaklis, P.J.: Information consensus of asynchronous discrete-time multi-agent systems. In: Proceedings of the 2005, American Control Conference, pp. 1883–1888. IEEE (2005)Google Scholar
  18. 18.
    Fehnker, A., Ivančić, F.: Benchmarks for hybrid systems verification. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 326–341. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-24743-2_22CrossRefzbMATHGoogle Scholar
  19. 19.
    Flanagan, C., Godefroid, P.: Dynamic partial-order reduction for model checking software. In: ACM Sigplan Notices, vol. 40, pp. 110–121. ACM (2005)CrossRefGoogle Scholar
  20. 20.
    Godefroid, P. (ed.): Partial-Order Methods for the Verification of Concurrent Systems: An Approach to the State-Explosion Problem. LNCS, vol. 1032. Springer, Heidelberg (1996).  https://doi.org/10.1007/3-540-60761-7CrossRefzbMATHGoogle Scholar
  21. 21.
    Huang, Z., Fan, C., Mereacre, A., Mitra, S., Kwiatkowska, M.: Simulation-based verification of cardiac pacemakers with guaranteed coverage. IEEE Des. Test 32(5), 27–34 (2015)CrossRefGoogle Scholar
  22. 22.
    Huang, Z., Mitra, S.: Proofs from simulations and modular annotations. In: Proceedings of the 17th International Conference on Hybrid systems: Computation and Control, pp. 183–192. ACM (2014)Google Scholar
  23. 23.
    Kurshan, R., Levin, V., Minea, M., Peled, D., Yenigün, H.: Static partial order reduction. In: Steffen, B. (ed.) TACAS 1998. LNCS, vol. 1384, pp. 345–357. Springer, Heidelberg (1998).  https://doi.org/10.1007/BFb0054182CrossRefGoogle Scholar
  24. 24.
    Majumdar, R., Saha, I.: Symbolic robustness analysis. In: 30th IEEE Real-Time Systems Symposium, RTSS 2009, pp. 355–363. IEEE (2009)Google Scholar
  25. 25.
    Mitra, D.: An asynchronous distributed algorithm for power control in cellular radio systems. In: Holtzman, J.M., Goodman, D.J. (eds.) Wireless and Mobile Communications, pp. 177–186. Springer, Boston (1994)CrossRefGoogle Scholar
  26. 26.
    Mitra, S., Chandy, K.M.: A formalized theory for verifying stability and convergence of automata in PVS. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds.) TPHOLs 2008. LNCS, vol. 5170, pp. 230–245. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-71067-7_20CrossRefzbMATHGoogle Scholar
  27. 27.
    Olfati-Saber, R., Fax, J.A., Murray, R.M.: Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–233 (2007)CrossRefGoogle Scholar
  28. 28.
    Peled, D.: Ten years of partial order reduction. In: Hu, A.J., Vardi, M.Y. (eds.) CAV 1998. LNCS, vol. 1427, pp. 17–28. Springer, Heidelberg (1998).  https://doi.org/10.1007/BFb0028727CrossRefGoogle Scholar
  29. 29.
    Rhee, I.K., Lee, J., Kim, J., Serpedin, E., Wu, Y.C.: Clock synchronization in wireless sensor networks: an overview. Sensors 9(1), 56–85 (2009)CrossRefGoogle Scholar
  30. 30.
    Samanta, R., Deshmukh, J.V., Chaudhuri, S.: Robustness analysis of networked systems. In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) VMCAI 2013. LNCS, vol. 7737, pp. 229–247. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-35873-9_15CrossRefGoogle Scholar
  31. 31.
    Welch, J.L., Lynch, N.: A new fault-tolerant algorithm for clock synchronization. Inf. Comput. 77(1), 1–36 (1988)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Yang, Y., Chen, X., Gopalakrishnan, G., Kirby, R.M.: Efficient stateful dynamic partial order reduction. In: Havelund, K., Majumdar, R., Palsberg, J. (eds.) SPIN 2008. LNCS, vol. 5156, pp. 288–305. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-85114-1_20CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ECE DepartmentUniversity of Illinois at Urbana-ChampaignChampaignUSA

Personalised recommendations