Compositional Liveness-Preserving Conformance Testing of Timed I/O Automata

  • Lars LuthmannEmail author
  • Hendrik Göttmann
  • Malte Lochau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12018)


I/O conformance testing theories (e.g., ioco) are concerned with formally defining when observable output behaviors of an implementation conform to those permitted by a specification. Thereupon, several real-time extensions of ioco, usually called tioco, have been proposed, further taking into account permitted delays between actions. In this paper, we propose an improved version of tioco, called live timed ioco (ltioco), tackling various weaknesses of existing definitions. Here, a reasonable adaptation of quiescence (i.e., observable absence of any outputs) to real-time behaviors has to be done with care: ltioco therefore distinguishes safe outputs being allowed to happen, from live outputs being enforced to happen within a certain time period thus inducing two different facets of quiescence. Furthermore, tioco is frequently defined on Timed I/O Labeled Transition Systems (TIOLTS), a semantic model of Timed I/O Automata (TIOA) which is infinitely branching and thus infeasible for practical testing tools. Instead, we extend the theory of zone graphs to enable ltioco testing on a finite semantic model of TIOA. Finally, we investigate compositionality of ltioco with respect to parallel composition including a proper treatment of silent transitions.


Real-time testing Timed Automata Input/output conformance testing Compositionality 


  1. 1.
    Aceto, L., Burgueño, A., Larsen, K.G.: Model checking via reachability testing for timed automata. In: Steffen, B. (ed.) TACAS 1998. LNCS, vol. 1384, pp. 263–280. Springer, Heidelberg (1998). Scholar
  2. 2.
    Alur, R., Dill, D.: Automata for modeling real-time systems. In: Paterson, M.S. (ed.) ICALP 1990. LNCS, vol. 443, pp. 322–335. Springer, Heidelberg (1990). Scholar
  3. 3.
    Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994). Scholar
  4. 4.
    André, É.: What’s decidable about parametric timed automata? In: Artho, C., Ölveczky, P.C. (eds.) FTSCS 2015. CCIS, vol. 596, pp. 52–68. Springer, Cham (2016). Scholar
  5. 5.
    Bannour, B., Gaston, C., Aiguier, M., Lapitre, A.: Results for compositional timed testing. In: APSEC 2013, pp. 559–564. IEEE (2013).
  6. 6.
    Belinfante, A.: JTorX: a tool for on-line model-driven test derivation and execution. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 266–270. Springer, Heidelberg (2010). Scholar
  7. 7.
    Bellman, R.: Dynamic Programming. Princeton University Press, Princeton (1957)zbMATHGoogle Scholar
  8. 8.
    Bengtsson, J., Yi, W.: Timed automata: semantics, algorithms and tools. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) ACPN 2003. LNCS, vol. 3098, pp. 87–124. Springer, Heidelberg (2004). Scholar
  9. 9.
    Beohar, H., Mousavi, M.R.: Input–output conformance testing for software product lines. J. Log. Algebraic Methods Program. 85(6), 1131–1153 (2016). Scholar
  10. 10.
    Bérard, B., Petit, A., Diekert, V., Gastin, P.: Characterization of the expressive power of silent transitions in timed automata. Fundam. Inform. 36(2,3), 145–182 (1998). Scholar
  11. 11.
    Bernot, G.: Testing against formal specifications: a theoretical view. In: Abramsky, S., Maibaum, T.S.E. (eds.) TAPSOFT 1991. LNCS, vol. 494, pp. 99–119. Springer, Heidelberg (1991). Scholar
  12. 12.
    Bohnenkamp, H., Belinfante, A.: Timed testing with TorX. In: Fitzgerald, J., Hayes, I.J., Tarlecki, A. (eds.) FM 2005. LNCS, vol. 3582, pp. 173–188. Springer, Heidelberg (2005). Scholar
  13. 13.
    Bornot, S., Gößler, G., Sifakis, J.: On the construction of live timed systems. In: Graf, S., Schwartzbach, M. (eds.) TACAS 2000. LNCS, vol. 1785, pp. 109–126. Springer, Heidelberg (2000). Scholar
  14. 14.
    Briones, L.B., Brinksma, E.: A test generation framework for quiescent real-time systems. In: Grabowski, J., Nielsen, B. (eds.) FATES 2004. LNCS, vol. 3395, pp. 64–78. Springer, Heidelberg (2005). Scholar
  15. 15.
    Brandán Briones, L., Röhl, M.: Test derivation from timed automata. In: Broy, M., Jonsson, B., Katoen, J.-P., Leucker, M., Pretschner, A. (eds.) Model-Based Testing of Reactive Systems. LNCS, vol. 3472, pp. 201–231. Springer, Heidelberg (2005). Scholar
  16. 16.
    Broy, M., Jonsson, B., Katoen, J.-P., Leucker, M., Pretschner, A. (eds.): Model-Based Testing of Reactive Systems. LNCS, vol. 3472. Springer, Heidelberg (2005). Scholar
  17. 17.
    David, A., Larsen, K.G., Legay, A., Nyman, U., Wasowski, A.: Timed I/O automata: a complete specification theory for real-time systems. In: HSCC 2010, pp. 91–100. ACM (2010).
  18. 18.
    Dill, D.L.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 197–212. Springer, Heidelberg (1990). Scholar
  19. 19.
    En-Nouaary, A., Dssouli, R.: A guided method for testing timed input output automata. In: Hogrefe, D., Wiles, A. (eds.) TestCom 2003. LNCS, vol. 2644, pp. 211–225. Springer, Heidelberg (2003). Scholar
  20. 20.
    Guha, S., Narayan, C., Arun-Kumar, S.: On decidability of prebisimulation for timed automata. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 444–461. Springer, Heidelberg (2012). Scholar
  21. 21.
    Havelund, K., Skou, A., Larsen, K.G., Lund, K.: Formal modeling and analysis of an audio/video protocol: an industrial case study using UPPAAL. In: RTSS 1997, pp. 2–13 (1997).
  22. 22.
    Henzinger, T.A., Manna, Z., Pnueli, A.: Temporal proof methodologies for real-time systems. In: Proceedings of the 18th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 1991, pp. 353–366. ACM (1991).
  23. 23.
    Henzinger, T.A., Nicollin, X., Sifakis, J., Yovine, S.: Symbolic model checking for real-time systems. Inf. Comput. 111(2), 193–244 (1994). Scholar
  24. 24.
    Hessel, A., Larsen, K.G., Mikucionis, M., Nielsen, B., Pettersson, P., Skou, A.: Testing real-time systems using UPPAAL. In: Hierons, R.M., Bowen, J.P., Harman, M. (eds.) Formal Methods and Testing. LNCS, vol. 4949, pp. 77–117. Springer, Heidelberg (2008). Scholar
  25. 25.
    Jensen, H.E., Larsen, K.G., Skou, A.: Modelling and analysis of a collision avoidance protocol using SPIN and UPPAAL. In: DIMACS 1996 (1996)Google Scholar
  26. 26.
    Krichen, M., Tripakis, S.: Black-box conformance testing for real-time systems. In: Graf, S., Mounier, L. (eds.) SPIN 2004. LNCS, vol. 2989, pp. 109–126. Springer, Heidelberg (2004). Scholar
  27. 27.
    Larsen, K.G., Mikucionis, M., Nielsen, B.: Online testing of real-time systems using Uppaal. In: Grabowski, J., Nielsen, B. (eds.) FATES 2004. LNCS, vol. 3395, pp. 79–94. Springer, Heidelberg (2005). Scholar
  28. 28.
    Larsen, K.G., Mikucionis, M., Nielsen, B., Skou, A.: Testing real-time embedded software using UPPAAL-TRON: an industrial case study. In: EMSOFT 2005, pp. 299–306. ACM (2005).
  29. 29.
    Larsen, K.G., Pettersson, P., Yi, W.: Uppaal in a nutshell. Int. J. Softw. Tools Technol. Transf. 1(1), 134–152 (1997). Scholar
  30. 30.
    Lindahl, M., Pettersson, P., Yi, W.: Formal design and analysis of a gear controller. In: Steffen, B. (ed.) TACAS 1998. LNCS, vol. 1384, pp. 281–297. Springer, Heidelberg (1998). Scholar
  31. 31.
    Luthmann, L., Göttmann, H., Lochau, M.: Compositional liveness-preserving conformance testing of timed I/O automata. Technical report, arXiv (2019). arXiv:1909.03703
  32. 32.
    Luthmann, L., Mennicke, S., Lochau, M.: Towards an I/O conformance testing theory for software product lines based on modal interface automata. In: FMSPLE 2015, EPTCS, vol. 182, pp. 1–13. arXiv (2015).
  33. 33.
    Luthmann, L., Mennicke, S., Lochau, M.: Compositionality, decompositionality and refinement in input/output conformance testing. In: Kouchnarenko, O., Khosravi, R. (eds.) FACS 2016. LNCS, vol. 10231, pp. 54–72. Springer, Cham (2017). Scholar
  34. 34.
    Luthmann, L., Mennicke, S., Lochau, M.: Unifying modal interface theories and compositional input/output conformance testing. Sci. Comput. Program. 172, 27–47 (2019). Scholar
  35. 35.
    Lynch, N.A., Attiya, H.: Using mappings to prove timing properties. Distrib. Comput. 6(2), 121–139 (1992). Scholar
  36. 36.
    Merritt, M., Modugno, F., Tuttle, M.R.: Time-constrained automata. In: Baeten, J.C.M., Groote, J.F. (eds.) CONCUR 1991. LNCS, vol. 527, pp. 408–423. Springer, Heidelberg (1991). Scholar
  37. 37.
    Pettersson, P.: Modelling and verification of real-time systems using timed automata: theory and practice. Ph.D. thesis (1999)Google Scholar
  38. 38.
    Rokicki, T.G.: Representing and modeling digital circuits. Ph.D. thesis (1994)Google Scholar
  39. 39.
    Schmaltz, J., Tretmans, J.: On conformance testing for timed systems. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 250–264. Springer, Heidelberg (2008). Scholar
  40. 40.
    Springintveld, J., Vaandrager, F.W., D’Argenio, P.R.: Testing timed automata. Theor. Comput. Sci. 254(1), 225–257 (2001). Scholar
  41. 41.
    von Styp, S., Bohnenkamp, H., Schmaltz, J.: A conformance testing relation for symbolic timed automata. In: Chatterjee, K., Henzinger, T.A. (eds.) FORMATS 2010. LNCS, vol. 6246, pp. 243–255. Springer, Heidelberg (2010). Scholar
  42. 42.
    Tretmans, J.: Test generation with inputs, outputs and repetitive quiescence (1996).
  43. 43.
    Tretmans, J., Brinksma, E.: TorX: automated model-based testing, pp. 31–43 (2003)Google Scholar

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Authors and Affiliations

  1. 1.Real-Time Systems LabTU DarmstadtDarmstadtGermany

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