Abstract
This paper describes the modeling, done using the Event-B notation, of the aircraft landing gear case study that was proposed in a special track of the ABZ’2014 Conference. In the course of our development, we discovered some problems in our initial modeling approach. This has led us to propose a second approach and then a third one. Each approach is more efficient than the previous one in terms of proof obligations (roughly speaking: 2000, 1000, 500). All this will be described in this paper. The methodology of proving reachability and deadlock freeness are discussed. Animation and simulation are used as complementary analysis to formal proofs. We also try to go beyond this specific case study and give some thoughts about large industrial modeling.

















Similar content being viewed by others
References
Rodin development for this Paper. http://www.cas.mcmaster.ca/~khedri/?page_id=778
Abrial, J.-R.: The B-Book: Assigning Programs to Meanings. Cambridge University Press, New York (1996)
Abrial, J.-R.: Modeling in Event-B: System and Software Engineering. Cambridge University Press, New York (2010)
Abrial, J.-R., Butler, M.J., Hallerstede, S., Hoang, T.S., Mehta, Farhad, Voisin, Laurent: Rodin: an open toolset for modelling and reasoning in Event-B. STTT 12(6), 447–466 (2010)
Abrial, J.-R., Mussat, L.: Introducing dynamic constraints in B. In: Proceedings of B’98: Recent Advances in the Development and Use of the B Method, 2nd International B Conference, Montpellier, 22–24 April 1998, pp. 83–128 (1998)
Abrial, J.-R., Su, W., Zhu, H.: Formalizing hybrid systems with Event-B. In: ABZ, pp. 178–193 (2012)
Anim, B. http://www.animb.org
Atelier, B.: http://www.atelierb.eu
Barrett, C.W., de Moura, L., Stump, A.: Smt-comp: satisfiability modulo theories competition. In: Proceedings of 17th International Conference on Computer Aided Verification, Lecture Notes in Computer Science, vol. 357, Edinburgh, Scotland, 6–10 July 2005
Boniol, F., Wiels, V.: The Landing Gear System Case Study. In: ABZ Case Study. Communications in Computer Information Science, vol. 433. Springer (2014)
Boström, P.: Creating sequential programs from Event-B models. In: Proceedings of, 8th International Conference on Integrated Formal Methods, pp. 74–88. Nancy, 11–14 Oct 2010
Bozzano, M., Bruttomesso, R., Cimatti, A., Junttila, T., Ranise, S., van Rossum, P., Sebastiani, R.: Efficient satisfiability modulo theories via delayed theory combination. In: Proceedings of the 17th International Conference on Computer Aided Verification, pp. 335–349 (2005)
Cansell, D., Méry, D., Rehm, J.: Time constraint patterns for Event-B development. In: Proceedings of B 2007: Formal Specification and Development in B, 7th International Conference of B Users, pp. 140–154. Besançon, 17–19 January 2007
Peter, F., Vadim, E.: Modelica—a unified object-oriented language for system modelling and simulation. In Proceedings of ECOOP’98—Object-Oriented Programming, 12th European Conference, pp. 67–90. Brussels, 20-24 July 1998
Fürst A., Hoang, T.S., Basin, D.A., Desai, K., Sato, N., Miyazaki, K.: Code generation for Event-B. In: Proceedings of 11th International Conference on Integrated Formal Methods, pp. 323–338. Bertinoro, 9–11 Sept 2014
Hallerstede, S., Jastram, M., Ladenberger, L.: A method and tool for tracing requirements into specifications. Science of Computer Programming, p. 36 (2013)
Hallerstede, S., Jastram, M., Ladenberger, L.: A method and tool for tracing requirements into specifications. Sci. Comput. Program. 82, 2–21 (2014)
Hallerstede, S., Leuschel, M.: Constraint-based deadlock checking of high-level specifications. TPLP 11(4–5), 767–782 (2011)
Hoang, T.S., Abrial, J.-R.: Reasoning about liveness properties in Event-B. In: Proceedings of 13th International Conference on Formal Engineering Methods on Formal Methods and Software Engineering, pp. 456–471. Durham, 26–28 Oct 2011
Hoang, T.S., Fürst, A., Abrial, J.-R.: Event-B patterns and their tool support. Softw. Syst. Model. 12(2), 229–244 (2013)
Kuruma, H., Basin, D.A., Abrial, J.-R.: Developing topology discovery in Event-B. Sci. Comput. Program. 74(11–12), 879–899 (2009)
Hudon, S., Hoang, T.S.: Development of control systems guided by models of their environment. Electron. Notes Theor. Comput. Sci. 280, 57–68 (2011)
Larman, C.: Applying UML and Patterns: An Introduction to Object-Oriented Analysis and Design and Iterative Development. Prentice Hall, Upper Saddle River (2004)
Leuschel, M., Butler, M.J.: ProB: an automated analysis toolset for the B method. STTT 10(2), 185–203 (2008)
Manna, Z., Pnueli, A.: Adequate proof principles for invariance and liveness properties of concurrent programs. Sci. Comput. Program. 4(3), 257–289 (1984)
Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems Specification. Springer, New York (1992)
Manna, Z., Pnueli, A.: Temporal Verification of Reactive Systems Safety. Springer, New York (1995)
MathWorks. http://www.mathworks.com/
Méry, D., Singh, N.K.: Automatic code generation from Event-B models. In: Proceedings of the 2011 Symposium on Information and Communication Technology, Hanoi, pp. 179–188. 13–14 Oct 2011
Otter, M., Malmheden, M., Elmqvist, H., Mattsson, S.E., Johnsson, C.: A new formalism for modeling of reactive and hybrid systems. In: 7th international Modelica Conference, pp. 364–377 (2009)
Rodin. http://www.event-b.org/
Said, M.Y., Butler, M.J., Snook, C.F.: Language and tool support for class and state machine refinement in UML-B. In: Proceedings of Formal Methods, Second World Congress, Eindhoven, pp. 579–595. 2–6 Nov 2009
Sarshogh, M.R., Butler, M.J.: Specification and refinement of discrete timing properties in Event-B. ECEASST, vol. 46 (2011)
Savicks, V., Butler, M., Colley, J.: Co-simulation environment for Rodin: landing gear case study. In: ABZ 2014: The Landing Gear Case Study, pp. 148–153 (2014)
Wen, S., Abrial J.-R., Runlei, H., Huibiao, Z.: From requirements to development: Methodology and example. In: ICFEM, pp. 437–455 (2011)
Su W., Abrial J.-R., Zhu H.: Complementary methodologies for developing hybrid systems with Event-B. In: ICFEM, pp. 230–248 (2012)
Voisin, L., Abrial, J.-R.: The rodin platform has turned ten. In: Proceedings of Abstract State Machines, Alloy, B, TLA, VDM, and Z - 4th International Conference, ABZ 2014, pp. 1–8. Toulouse, 2–6 June 2014
Yeganefard, S., Butler, M.J., Rezazadeh, A.: Evaluation of a guideline by formal modelling of cruise control system in Event-B. In: Proceedings of Second NASA Formal Methods Symposium—NFM 2010, pp. 182–191. Washington D.C., 13–15 April 2010
Acknowledgments
Wen Su was supported in part by the Science and Technology Commission of Shanghai Municipality (Grant No. 15YF1403900), the Open Project of Shanghai Key Laboratory of Trustworthy Computing (Grant No. 07dz22304201303) and National Natural Science Foundation of China (Grant No. 61402176).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Su, W., Abrial, JR. Aircraft landing gear system: approaches with Event-B to the modeling of an industrial system. Int J Softw Tools Technol Transfer 19, 141–166 (2017). https://doi.org/10.1007/s10009-015-0400-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10009-015-0400-3