Probabilistic verification and synthesis of the next generation airborne collision avoidance system

  • Christian von Essen
  • Dimitra GiannakopoulouEmail author
TACAS 2014


The next generation airborne collision avoidance system, ACAS X, departs from the traditional deterministic model on which the current system, TCAS, is based. To increase robustness, ACAS X relies on probabilistic models to represent the various sources of uncertainty. The work reported in this paper identifies verification challenges for ACAS X, and studies the applicability of probabilistic verification and synthesis techniques in addressing these challenges. Due to shortcomings of off-the-shelf probabilistic analysis tools, we developed a new framework, named VeriCA (Verification for Collision Avoidance). VeriCA is a combined probabilistic synthesis and verification framework that is custom designed for ACAS X and systems with similar characteristics. VeriCA supports Java as a modeling language, is memory efficient, employs parallelization, and provides an interactive simulator that displays aircraft encounters and the corresponding ACAS X behavior. We describe the application of our framework to ACAS X, together with the results and recommendations that our analysis produced.


Markov decision processes Probabilistic verification  Probabilistic synthesis Aircraft collision avoidance 



We wish to thank Neal Suchy of the FAA for being supportive of this work and putting us in contact with ACAS X team members. In particular, Mykel Kochenderfer helped us ensure that our ACAS X model was faithful to the one in the published version, and Ryan Gardner and Yanni Kouskoulas helped us identify verification and synthesis challenges through extensive discussions. Finally, we thank Guillaume Brat for providing technical feedback for this work, and Johann Schumann, Mykel Kochenderfer, and Ryan Gardner for proof-reading the paper. The work was funded under the System-wide Safety Analysis Technologies Project of the Aviation Safety Program in NASA ARMD.


  1. 1.
    Chatterjee, K., Majumdar, R., Henzinger, T.A.: Markov decision processes with multiple objectives. In: STACS 2006, 23rd Annual Symposium on Theoretical Aspects of Computer Science, Marseille, France, February 23–25, 2006, pp. 325–336 (2006)Google Scholar
  2. 2.
    Forejt, V., Kwiatkowska, M., Parker, D.: Pareto curves for probabilistic model checking. In: Chakraborty, S., Mukund, M. (eds.) Proc. 10th International Symposium on Automated Technology for Verification and Analysis (ATVA’12), volume 7561 of LNCS, pp. 317–332. Springer (2012)Google Scholar
  3. 3.
    Galdino, A.L., Muñoz, C., Ayala-Rincón, M.: Formal verification of an optimal air traffic conflict resolution and recovery algorithm. In: Logic, Language, Information and Computation, 14th International Workshop, WoLLIC 2007, Rio de Janeiro, Brazil, July 2–5, 2007, pp. 177–188 (2007)Google Scholar
  4. 4.
    Ghorbal, K., Jeannin, J., Zawadzki, E., Platzer, A., Gordon, G.J., Capell, P.: Hybrid theorem proving of aerospace systems: Applications and challenges. J. Aerospace Inf. Sys. 11(10), 702–713 (2014)CrossRefGoogle Scholar
  5. 5.
    Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects Comp. 6, 102–111 (1994)zbMATHGoogle Scholar
  6. 6.
    Jeannin, J., Ghorbal, K., Kouskoulas, Y., Gardner, R., Schmidt, A., Zawadzki, E., Platzer, A.: A formally verified hybrid system for the next-generation airborne collision avoidance system. In: Tools and Algorithms for the Construction and Analysis of Systems - 21st International Conference, TACAS 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015, London, UK, April 11–18, 2015, pp. 21–36 (2015)Google Scholar
  7. 7.
    Julier, S.J., Uhlmann, J.K.: Unscented filtering and nonlinear estimation. Proc. IEEE 92(3), 401–422 (2004)CrossRefGoogle Scholar
  8. 8.
    Katoen, J., Zapreev, I.S., Hahn, E.M., Hermanns, H., Jansen, D.N.: The ins and outs of the probabilistic model checker MRMC. Perform. Eval. 68(2), 90–104 (2011)CrossRefGoogle Scholar
  9. 9.
    Kochenderfer, M.J.: Decision making under uncertainty: theory and application. MIT Press, Cambridge (2015). Please cehck and confirm the publisher location is correct and amend if necessaryzbMATHGoogle Scholar
  10. 10.
    Kochenderfer, M.J., Chryssanthacopoulos, J.P.: Robust airborne collision avoidance through dynamic programming. Project Report ATC-371, Massachusetts Institute of Technology, Lincoln Laboratory (2011)Google Scholar
  11. 11.
    Kuchar, J., Drumm, A.C.: The traffic alert and collision avoidance system. Lincoln Lab. J. 16(2), 277 (2007)Google Scholar
  12. 12.
    Kwiatkowska, M.Z., Norman, G., Parker. D.: PRISM 4.0: Verification of probabilistic real-time systems. In: Computer Aided Verification - 23rd International Conference, CAV 2011, Snowbird, UT, USA, July 14–20, 2011, pp. 585–591 (2011)Google Scholar
  13. 13.
    Loos, S.M., Renshaw, D.W., Platzer, A.: Formal verification of distributed aircraft controllers. In: Proceedings of the 16th international conference on Hybrid systems: computation and control, HSCC 2013, April 8–11, 2013, Philadelphia, PA, USA, pp. 125–130 (2013)Google Scholar
  14. 14.
    Lygeros, J., Lynch, N.: On the formal verification of the TCAS conflict resolution algorithms. In: 36th IEEE Conference on Decision and Control, pp. 1829–1834 (1997)Google Scholar
  15. 15.
    Platzer, A., Clarke E.M.: Formal verification of curved flight collision avoidance maneuvers: A case study. In: FM 2009: Formal Methods, Second World Congress, Eindhoven, The Netherlands, November 2–6, 2009, pp. 547–562 (2009)Google Scholar
  16. 16.
    Rennen, G., van Dam, E.R., den Hertog, D.: Enhancement of sandwich algorithms for approximating higher-dimensional convex Pareto sets. INFORMS J. Comp. 23(4), 493–517 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Tomlin, C., Pappas, G.J., Sastry, S.: Conflict resolution for air traffic management: A study in multiagent hybrid systems. IEEE Trans. Auto. Cont. 43(4), 509–521 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    von Essen C.: Quantitative Verification and Synthesis. PhD Thesis, Université Joseph Fourier, Grenoble, France (2014)Google Scholar
  19. 19.
    von Essen, C., Giannakopoulou, D.: Analyzing the next generation airborne collision avoidance system. In: Tools and Algorithms for the Construction and Analysis of Systems - 20th International Conference, TACAS 2014, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2014, Grenoble, France, April 5–13, 2014, pp. 620–635 (2014)Google Scholar
  20. 20.
    Zuliani, P., Platzer, A., Clarke, E.M.: Bayesian statistical model checking with application to Stateflow/Simulink verification. Formal Methods Syst. Design 43(2), 338–367 (2013)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg (outside the USA) 2015

Authors and Affiliations

  1. 1.VerimagGrenobleFrance
  2. 2.NASA Ames Research CenterMoffett FieldUSA

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