A loop acceleration technique to speed up verification of automatically generated plans

  • Robert P. Goldman
  • Michael J. S. PelicanEmail author
  • David J. Musliner


The CIRCA planning system automatically creates reactive plans and uses formal verification techniques to prove that those plans will preserve system safety. CIRCA’s timed automata verification system is highly efficient, yet can display pathologically bad behavior when reasoning about reaction loops, a particular form of interacting cycles of states. In this paper, we describe a loop acceleration technique that recognizes these state-space structures during the verification process and bypasses the process of expanding an arbitrarily large cycle of states, effectively compressing loops of arbitrary size into a compact, finite set of states. The resulting performance improvement can be very dramatic: in domains where tight loops of short-duration transitions interact with long-duration transitions, our new loop acceleration methods can reduce verification time (and hence planning time) from hours to below a second.


Automated planning Verification Model checking Timed automata Loop acceleration 



This article was supported by Office of Naval Research contract N0014-10-1-0188 via Carnegie Mellon University subaward number 1140185-240250 and Air Force Office of Scientific Research contract FA9550-12-1-0146 via Carnegie Mellon University subaward number 1150105-284227. This paper does not represent the official position or opinions of the Office of Naval Research, the Air Force Office of Scientific Research, or Carnegie Mellon University. Thanks to Ed Koeller for collecting supporting images and data. Thanks to our reviewers for many helpful questions, suggestions, and corrections.


  1. 1.
    Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126, 183–235 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Larsen, K.G., Pettersson, P., Yi, W.: Model-checking for real-time systems. In: Proceedings of Fundamentals of Computation Theory. Lecture Notes in Computer Science, vol. 965, pp. 62–88 (1995)Google Scholar
  3. 3.
    Behrmann, G., Bengtsson, J., David, A., Larsen, K.G., Pettersson, P., Yi, W.: Uppaal implementation secrets. In: Proceedings of 7th International Symposium on Formal Techniques in Real-Time and Fault Tolerant Systems (2002)Google Scholar
  4. 4.
    Behrmann, G., David, A., Larsen, K.G.: A tutorial on uppaal. In: Bernardo, M., Corradini, F. (eds.) Formal Methods for the Design of Real-Time Systems: 4th International School on Formal Methods for the Design of Computer, Communication, and Software Systems, SFM-RT 2004, vol. 3185 in LNCS, pp. 200–236. Springer, Berlin (2004)Google Scholar
  5. 5.
    Yovine, S.: Kronos: a verification tool for real-time sytems. Springer Int J Softw Tools Technol Transf. 1, 123–133 (1997)Google Scholar
  6. 6.
    Hune, T.S.: Modeling a language for embedded systems in timed automata. Research Series RS-00-17, BRICS, Department of Computer Science, University of Aarhus, Aug. 2000, 26 pp. Earlier version entitled Modelling a Real-Time Language appeared in Fourth International Workshop on Formal Methods for Industrial Critical Systems (FMICS99), pp. 259–282 (2000)Google Scholar
  7. 7.
    Iversen, T.K., Kristoffersen, K.J., Larsen, K.G., Laursen, M., Madsen, R.G., Mortensen, S.K., Pettersson, P., Thomasen, C.B.: Model-checking real-time control programs—verifying LEGO MINDSTORMS systems using UPPAAL. In: Proceedings of 12th Euromicro Conference on Real-Time Systems, pp. 147–155. IEEE Computer Society Press, New York (2000)Google Scholar
  8. 8.
    Hendriks, M., Larsen, K.G.: Exact acceleration of real-time model checking. Electronic Notes in Theoretical Computer Science, vol. 65 (2002)Google Scholar
  9. 9.
    Musliner, D.J., Durfee, E.H., Shin, K.G.: CIRCA: a cooperative intelligent real-time control architecture. IEEE Trans. Syst. Man Cybern. 23(6), 1561–1574 (1993)CrossRefGoogle Scholar
  10. 10.
    Musliner, D.J., Durfee, E.H., Shin, K.G.: World modeling for the dynamic construction of real-time control plans. Artif. Intell. 74, 83–127 (1995)CrossRefGoogle Scholar
  11. 11.
    Musliner, D.J., Pelican, M.J.S., Goldman, R.P., Krebsbach, K.D., Durfee, E.H.: The evolution of CIRCA, a theory-based AI architecture with real-time performance guarantees. In: AAAI Spring Symposium on Architectures for Intelligent Theory-Based Agents (2008)Google Scholar
  12. 12.
    Kortenkamp, D., Bonasso, P., Musliner, D.J., Pelican, M.J.S., Hostetler, J.: Embedding planning technology into satellite systems. In: AIAA Infotech@Aerospace (2011)Google Scholar
  13. 13.
    Hendriks, M.: Model Checking Timed Automata—Techniques and Applications. PhD thesis, Institute for Programming research and Algorithmics (IPA) (2006)Google Scholar
  14. 14.
    Fietzke, A., Kruglov, E., Weidenbach, C.: Automatic generation of inductive invariants by sup(la). Tech. Rep. MPII2012RG1-002, Max-Planck-Institut fur Informatik (2012)Google Scholar
  15. 15.
    Bozga, M., Konecny, F., Iosif, R.: Fast acceleration of ultimately periodic relations, Tech. Rep. TR-2010-3, Verimag Technical Report, 2010. Version: 1 (2010)Google Scholar
  16. 16.
    Bardin, S., Finkel, A., Leroux, J., Schnoebelen, P.: Flat acceleration in symbolic model checking. In: Peled, D.A., Tsay, Y.-K. (eds.) Proceedings of the 3rd International Symposium on Automated Technology for Verification and Analysis (ATVA’05), Lecture Notes in Computer Science, vol. 3707, pp. 474–488. Springer, Taipei, Taiwan (2005)Google Scholar
  17. 17.
    Bardin, S., Leroux, J., Point, G.: FAST extended release. In: Ball, T., Jones, R.B. (eds.) Computer Aided Verification (CAV). Lecture Notes in Computer Science, vol. 4144 , pp. 63–66. Springer, Berlin (2006)Google Scholar
  18. 18.
    Salah, R.B.: On Timing Analysis Of Large Systems. PhD thesis, Institut National Polytechnique De Grenoble (2007)Google Scholar
  19. 19.
    Gat, E.: News from the trenches: an overview of unmanned spacecraft for AI. In: Nourbakhsh, I. (ed.) AAAI Technical Report SSS-96-04: Planning with Incomplete Information for Robot Problems. American Association for Artificial Intelligence (1996)Google Scholar
  20. 20.
    Musliner, D.J., Goldman, R.P.: CIRCA and the Cassini Saturn orbit insertion: Solving a prepositioning problem. In: Working Notes of the NASA Workshop on Planning and Scheduling for Space (1997) Google Scholar
  21. 21.
    Goldman, R.P., Pelican, M.J.S., Musliner, D.J.: Guiding planner backjumping using verifier traces. In: Zilberstein, S., Koehler, J., Koenig, S. (eds.) Proceedings of the Fourteenth International Conference on Automated Planning and Scheduling, pp. 279–286 (2004)Google Scholar
  22. 22.
    Potts, C.M., Krebsbach, K.D., Thayer, J.T., Musliner, D.J.: Improving trust estimates in planning domains with rare failure events. In: AAAI Spring Symposium on Trust and Autonomous Systems (2013)Google Scholar
  23. 23.
    Kortenkamp, D., Hudson, M.B., Bell, S., Musliner, D.J., Pelican, M.J.S., Hamell, J., Zetocha, P.: Embedding planning technology into satellite systems. In: International Symposium on Artificial Intelligence, Robotics and Automation in Space (2012)Google Scholar
  24. 24.
    Daws, C., Olivero, A., Tripakis, S., Yovine, S.: The tool kronos. In: Hybrid Systems III: Verification and, Control, pp. 208–219 (1996)Google Scholar
  25. 25.
    Alur, R.: Timed automata. Tech. Rep. MS-CIS-98-10, University of Pennsylvania, Philadelphia (1998)Google Scholar
  26. 26.
    Alur, R.: Timed automata. In: Working Notes of the NATO-ASI Summer School on Verification of Digital and Hybrid Systems (1998)Google Scholar
  27. 27.
    Dill, D.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) Automatic Verification Methods for Finite State Systems. Lecture Notes in Computer Science, vol. 407 , pp. 197–212. Springer, Berlin (1990)Google Scholar
  28. 28.
    Dechter, R., Meiri, I., Pearl, J.: Temporal constraint networks. Artif. Intell. 49(1–3), 61–95 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  29. 29.
    Ramadge, P.J., Wonham, W.M.: The control of discrete event systems. Proc. IEEE 77, 81–98 (1989)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Robert P. Goldman
    • 1
  • Michael J. S. Pelican
    • 1
    Email author
  • David J. Musliner
    • 1
  1. 1.SIFT, LLCMinneapolisUSA

Personalised recommendations