Time-Bounded Reachability Problem for Recursive Timed Automata is Undecidable

  • Shankara Narayanan Krishna
  • Lakshmi ManasaEmail author
  • Ashutosh Trivedi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8977)


Motivated by the success of bounded model checking framework for finite state machines, Ouaknine and Worrell proposed a time-bounded theory of real-time verification by claiming that restriction to bounded-time recovers decidability for several key decision problem related to real-time verification. In support of this theory, the list of undecidable problems recently shown decidable under time-bounded restriction is rather impressive: language inclusion for timed automata, emptiness problem for alternating timed automata, and emptiness problem for rectangular hybrid automata. The objective of our study was to recover decidability for general recursive timed automata(RTA)—and perhaps for recursive hybrid automata—under time-bounded restriction in order to provide an appealing verification framework for powerful modeling environments such as Stateflow/Simulink. Unfortunately, however, we answer this question in negative by showing that time-bounded reachability problem stays undecidable for RTA with 5 clocks.


Recursive state machines Timed automata Reachability 


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  1. 1.
    Abdulla, P.A., Atig, M.F., Stenman, J.: Dense-timed pushdown automata. In: Proceedings of the 27th Annual IEEE Symposium on Logic in Computer Science. LICS, pp. 35–44 (2012)Google Scholar
  2. 2.
    Alur, R., Benedikt, M., Etessami, K., Godefroid, P., Reps, T., Yannakakis, M.: Analysis of recursive state machines. ACM Trans. Program. Lang. Syst. 27(4), 786–818 (2005)CrossRefGoogle Scholar
  3. 3.
    Alur, R., Dill, D.: Automata for modeling real-time systems. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 322–335. Springer, Heidelberg (1990) CrossRefGoogle Scholar
  4. 4.
    Ball, T., Rajamani, S.K.: Bebop: A symbolic model checker for boolean programs. In: Havelund, K., Penix, J., Visser, W. (eds.) SPIN 2000. LNCS, vol. 1885, pp. 113–130. Springer, Heidelberg (2000) CrossRefGoogle Scholar
  5. 5.
    Benerecetti, M., Minopoli, S., Peron, A.: Analysis of timed recursive state machines. In: Proceedings of 17th International Symposium on Temporal Representation and Reasoning TIME, pp. 61–68 (2010)Google Scholar
  6. 6.
    Mazurkiewicz, A., Winkowski, J.: Reachability analysis of pushdown automata: Application to model-checking. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol. 1243, pp. 135–150. Springer, Heidelberg (1997) Google Scholar
  7. 7.
    Esparza, J., Hansel, D., Rossmanith, P., Schwoon, S.: Efficient algorithms for modelchecking pushdown systems. In: Emerson, E., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 232–247. Springer, Heidelberg (2000) CrossRefGoogle Scholar
  8. 8.
    Harel, D.: Statecharts: A visual formalism for complex systems. Sci. Comput. Program. 8(3), 231–274 (1987)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Krishna, S.N., Manasa, L., Trivedi, A.: Improved undecidability results for reachability games on recursive timed automata. In: Proceedings of Fifth International Symposium on Games, Automata, Logics and Formal Verification GandALF, pp. 245–259 (2014)Google Scholar
  10. 10.
    Minsky, M.L.: Computation: finite and infinite machines. Prentice-Hall, Inc. (1967)Google Scholar
  11. 11.
    Rumbaugh, J., Jacobson, I., Booch, G.: The unified modeling language reference manual. Addison-Wesley-Longman (1999)Google Scholar
  12. 12.
    Trivedi, A., Wojtczak, D.: Recursive timed automata. In: Bouajjani, A., Chin, W.-N. (eds.) ATVA 2010. LNCS, vol. 6252, pp. 306–324. Springer, Heidelberg (2010) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Shankara Narayanan Krishna
    • 1
  • Lakshmi Manasa
    • 1
    Email author
  • Ashutosh Trivedi
    • 1
  1. 1.Indian Institute of Technology BombayMumbaiIndia

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