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European Train Control System

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Logical Analysis of Hybrid Systems

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Synopsis

Complex physical systems have several degrees of freedom. They only work correctly when their control parameters obey corresponding constraints. Based on the informal specification of the European Train Control System (ETCS), we design a controller for its cooperation protocol. For the free parameters of the system, we successively identify constraints that are required to ensure collision freedom. We formally prove the parameter constraints to be sharp by characterising them equivalently in terms of reachability properties of the hybrid system dynamics. We use the calculus of our differential dynamic logic for hybrid systems and formally verify controllability, safety, liveness, and reactivity properties of the ETCS protocol that entail collision freedom. We prove that the ETCS protocol remains correct even in the presence of perturbation by disturbances in the dynamics.

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References

  1. Quesel, J.D.: A theorem prover for differential dynamic logic. Master’s thesis, University of Oldenburg, Department of Computing Science. Correct System Design Group (2007)

    Google Scholar 

  2. Meyer, R., Faber, J., Hoenicke, J., Rybalchenko, A.: Model checking duration calculus: A practical approach. Formal Aspects of Computing pp. 1–25 (2008). DOI 10.1007/s00165-008-0082-7

    Google Scholar 

  3. Alur, R., Henzinger, T.A., Ho, P.H.: Automatic symbolic verification of embedded systems. IEEE T. Software Eng. 22(3), 181–201 (1996)

    Article  Google Scholar 

  4. Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement for symbolic model checking. J. ACM 50(5), 752–794 (2003). DOI 10.1145/876638.876643

    Article  MathSciNet  Google Scholar 

  5. Cimatti, A., Roveri, M., Tonetta, S.: Requirements validation for hybrid systems. In: A. Bouajjani, O. Maler (eds.) CAV, LNCS, vol. 5643. Springer (2009). DOI 10.1007/ 978-3-642-02658-4_17

    Google Scholar 

  6. Frehse, G.: PHAVer: Algorithmic verification of hybrid systems past HyTech. In: Morari and Thiele [212], pp. 258–273. DOI 10.1007/b106766

    Google Scholar 

  7. Damm, W., Mikschl, A., Oehlerking, J., Olderog, E.R., Pang, J., Platzer, A., Segelken, M., Wirtz, B.: Automating verification of cooperation, control, and design in traffic applications. In: C.B. Jones, Z. Liu, J. Woodcock (eds.) Formal Methods and Hybrid Real-Time Systems, LNCS, vol. 4700, pp. 115–169. Springer (2007). DOI 10.1007/978-3-540-75221-9_6

    Google Scholar 

  8. ERTMS User Group: ERTMS/ETCS System requirements specification. http://www.era.europa.eu (2002)

  9. Frehse, G.: PHAVer: algorithmic verification of hybrid systems past HyTech. STTT 10(3), 263–279 (2008). DOI 10.1007/s10009-007-0062-x

    Article  MathSciNet  Google Scholar 

  10. Platzer, A., Quesel, J.D.: European Train Control System: A case study in formal verification. Tech. Rep. 54, Reports of SFB/TR 14 AVACS (2009). ISSN: 1860-9821, http://www.avacs.org.

  11. Batt, G., Belta, C., Weiss, R.: Model checking genetic regulatory networks with parameter uncertainty. In: Bemporad et al. 41, pp. 61–75. DOI 10.1007/978-3-540-71493-4_8

    Google Scholar 

  12. Platzer, A., Quesel, J.D.: KeYmaera: A hybrid theorem prover for hybrid systems. In: Armando et al. [18], pp. 171–178. DOI 10.1007/978-3-540-71070-7_15

    Google Scholar 

  13. Platzer, A., Quesel, J.D.: European Train Control System: A case study in formal verification. In: K. Breitman, A. Cavalcanti (eds.) ICFEM, LNCS, vol. 5885, pp. 246–265. Springer (2009). DOI 10.1007/978-3-642-10373-5_13

    Google Scholar 

  14. Henzinger, T.A.: The theory of hybrid automata. In: LICS, pp. 278–292. IEEE Computer Society, Los Alamitos (1996)

    Google Scholar 

  15. Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: POPL, pp. 179–190 (1989). DOI 10.1145/75277.75293

    Google Scholar 

  16. Tomlin, C.J., Lygeros, J., Sastry, S.: A game theoretic approach to controller design for hybrid systems. Proc. IEEE 88(7), 949–970 (2000). DOI 10.1109/5.871303

    Article  Google Scholar 

  17. Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching-time temporal logic. In: D. Kozen (ed.) Logic of Programs, LNCS, vol. 131, pp. 52–71. Springer (1981)

    Google Scholar 

  18. Mysore, V., Piazza, C., Mishra, B.: Algorithmic algebraic model checking II: Decidability of semi-algebraic model checking and its applications to systems biology. In: Peled and Tsay [226], pp. 217–233. DOI 10.1007/11562948_18

    Google Scholar 

  19. Frehse, G., Jha, S.K., Krogh, B.H.: A counterexample-guided approach to parameter synthesis for linear hybrid automata. In: Egerstedt and Mishra [111], pp. 187–200. DOI 10.1007/978-3-540-78929-1_14

    Google Scholar 

  20. Lafferriere, G., Pappas, G.J., Sastry, S.: O-minimal hybrid systems. Mathematics of Control, Signals, and Systems 13(1), 1–21 (2000). DOI 10.1007/PL00009858

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Computer Science, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA, 15213, USA

    Dr. André Platzer

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  1. Dr. André Platzer
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Correspondence to André Platzer .

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Platzer, A. (2010). European Train Control System. In: Logical Analysis of Hybrid Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14509-4_7

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  • DOI: https://doi.org/10.1007/978-3-642-14509-4_7

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  • Print ISBN: 978-3-642-14508-7

  • Online ISBN: 978-3-642-14509-4

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