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Multi-agent Safety Verification Using Symmetry Transformations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12078)

Abstract

We show that symmetry transformations and caching can enable scalable, and possibly unbounded, verification of multi-agent systems. Symmetry transformations map any solution of the system to another solution. We show that this property can be used to transform cached reachsets to compute new reachsets, for hybrid and multi-agent models. We develop a notion of a virtual system which defines symmetry transformations for a broad class of agent models that visit waypoint sequences. Using this notion of a virtual system, we present a prototype tool CacheReach that builds a cache of reachsets, in a way that is agnostic of the representation of the reachsets and the reachability analysis method used. Our experimental evaluation of CacheReach shows up to 64% savings in safety verification computation time on multi-agent systems with 3-dimensional linear and 4-dimensional nonlinear fixed-wing aircraft models following sequences of waypoints. These savings and our theoretical results illustrate the potential benefits of using symmetry-based caching in the safety verification of multi-agent systems.

The authors are supported by a research grant from The Boeing Company and a research grant from NSF (CPS 1739966). We would like to thank John L. Olson and Arthur S. Younger from The Boeing Company for valuable technical discussions.

References

  1. Althoff, M.: An introduction to cora 2015. In: Proc. of the Workshop on Applied Verification for Continuous and Hybrid Systems (2015)

    Google Scholar 

  2. Althoff, M., Dolan, J.M.: Online verification of automated road vehicles using reachability analysis. IEEE Trans. Robotics 30(4), 903–918(2014). https://doi.org/10.1109/TRO.2014.2312453

  3. Bak, S., Duggirala, P.S.: Hylaa: A tool for computing simulation-equivalent reachability for linear systems. In: Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control. pp. 173–178. ACM (2017)

    Google Scholar 

  4. Bak, S., Tran, H., Johnson, T.T.: Numerical verification of affine systems with up to a billion dimensions. In: Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2019, Montreal,QC, Canada, April 16-18, 2019. pp. 23–32 (2019). https://doi.org/10.1145/3302504.3311792

  5. Bonnabel, S., Martin, P., Rouchon, P.: Symmetry-preserving observers. IEEE Transactions on Automatic Control 53(11), 2514–2526 (2008)

    Google Scholar 

  6. Chen, X.: Reachability analysis of non-linear hybrid systems using taylor models (2015)

    Google Scholar 

  7. Chen, X., Ábrahám, E., Sankaranarayanan, S.: Flow*: An analyzer for non-linear hybrid systems. In: Sharygina, N., Veith, H. (eds.) Computer Aided Verification, Lecture Notes in Computer Science, vol. 8044, pp. 258–263. Springer Berlin Heidelberg (2013)

    Google Scholar 

  8. Donzé, A.: Breach, a toolbox for verification and parameter synthesis of hybrid systems. In: Computer Aided Verification (CAV 2010), Lecture Notes in Computer Science, vol. 6174, pp. 167–170. Springer (2010)

    Google Scholar 

  9. Donzé, A., Maler, O.: Systematic simulation using sensitivity analysis. In: Hybrid Systems: Computation and Control, pp. 174–189. Springer (2007)

    Google Scholar 

  10. Duggirala, P.S., Fan, C., Mitra, S., Viswanathan, M.: Meeting a powertrain verification challenge. In: Computer Aided Verification - 27th International Conference, CAV 2015, San Francisco, CA, USA, July 18-24, 2015,Proceedings, Part I. pp. 536–543 (2015). https://doi.org/10.1007/978-3-319-21690-4_37

  11. Duggirala, P.S., Mitra, S., Viswanathan, M.: Verification of annotated models from executions. In: EMSOFT (2013)

    Google Scholar 

  12. Duggirala, P.S., Mitra, S., Viswanathan, M., Potok, M.: C2e2: A verification tool for stateflow models. In: Baier, C., Tinelli, C. (eds.) Tools and Algorithms for the Construction and Analysis of Systems. pp. 68–82. Springer Berlin Heidelberg, Berlin, Heidelberg (2015)

    Google Scholar 

  13. Duggirala, P.S., Viswanathan, M.: Parsimonious, simulation based verification of linear systems. In: Computer Aided Verification - 28th International Conference, CAV 2016, Toronto, ON, Canada, July 17-23, 2016, Proceedings, Part I. pp. 477–494 (2016). https://doi.org/10.1007/978-3-319-41528-4_26

  14. Fan, C., Kapinski, J., Jin, X., Mitra, S.: Locally optimal reach set over-approximation for nonlinear systems. In: EMSOFT. pp. 6:1–6:10. ACM (2016)

    Google Scholar 

  15. Fan, C., Mitra, S.: Bounded verification with on-the-fly discrepancy computation. In: ATVA. Lecture Notes in Computer Science, vol. 9364, pp.446–463. Springer (2015)

    Google Scholar 

  16. Fan, C., Qi, B., Mitra, S.: Data-driven formal reasoning and their applications in safety analysis of vehicle autonomy features. IEEE Design & Test35(3), 31–38 (2018). https://doi.org/10.1109/MDAT.2018.2799804

  17. Fan, C., Qi, B., Mitra, S., Viswanathan, M.: Data-driven verification andc ompositional reasoning for automotive systems. In: Computer Aided Verification. pp. 441–461. Springer International Publishing (2017)

    Google Scholar 

  18. Fan, C., Qi, B., Mitra, S., Viswanathan, M., Duggirala, P.S.: Automatic reachability analysis for nonlinear hybrid models with C2E2. In: Computer Aided Verification - 28th International Conference, CAV 2016, Toronto, ON, Canada, July 17-23, 2016, Proceedings, Part I. pp. 531–538 (2016). https://doi.org/10.1007/978-3-319-41528-4_29

  19. G’erard, L., Slotine, J.J.E.: Neuronal networks and controlled symmetries, a generic framework (2006)

    Google Scholar 

  20. Hartmanns, A., Seidl, M.: tacas20ae.ova. figshare (2019). https://doi.org/10.6084/m9.figshare.9699839.v2

  21. Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? Journal of Computer and System Sciences 57(1), 94– 124 (1998), http://www.sciencedirect.com/science/article/pii/S0022000098915811

  22. Johnson, T., Mitra, S.: A small model theorem for rectangular hybrid automata networks (2012)

    Google Scholar 

  23. Kushner, T., Bequette, B.W., Cameron, F., Forlenza, G.P., Maahs, D.M., Sankaranarayanan, S.: Models, devices, properties, and verification of artificial pancreas systems. In: Automated Reasoning for Systems Biology and Medicine, pp. 93–131 (2019). https://doi.org/10.1007/978-3-030-17297-8_4

  24. Mehta, P., Hagen, G., Banaszuk, A.: Symmetry and symmetry-breaking for a wave equation with feedback. SIAM J. Applied Dynamical Systems 6, 549–575 (01 2007). https://doi.org/10.1137/060666044

  25. Mitra, S.: Verifying Cyberphysical Systems: A path to safe autonomy. To be published by MIT Press, Cambridge, MA, USA (2020), https://sayanmitracode.github.io/cpsbooksite/

  26. Russo, G., Slotine, J.J.E.: Symmetries, stability, and control in nonlinear systems and networks. Physical Review E 84(4), 041929 (2011)

    Google Scholar 

  27. Sibai, H., Mokhlesi, N., Fan, C., Mitra, S.: Cachereach: multi-agent safety verification using symmetry transformations software tool (2020). https://doi.org/10.6084/m9.figshare.11874375

  28. Sibai, H., Mokhlesi, N., Mitra, S.: Using symmetry transformations in equivariant dynamical systems for their safety verification. In: Automated Technology for Verification and Analysis. pp. 1–17 (2019)

    Google Scholar 

  29. Spong, M.W., Bullo, F.: Controlled symmetries and passive walking. IEEE Transactions on Automatic Control 50(7), 1025–1031 (July 2005). https://doi.org/10.1109/TAC.2005.851449

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Sibai, H., Mokhlesi, N., Fan, C., Mitra, S. (2020). Multi-agent Safety Verification Using Symmetry Transformations. In: Biere, A., Parker, D. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2020. Lecture Notes in Computer Science(), vol 12078. Springer, Cham. https://doi.org/10.1007/978-3-030-45190-5_10

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  • DOI: https://doi.org/10.1007/978-3-030-45190-5_10

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