Reachability of Communicating Timed Processes

  • Lorenzo Clemente
  • Frédéric Herbreteau
  • Amelie Stainer
  • Grégoire Sutre
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7794)

Abstract

We study the reachability problem for communicating timed processes, both in discrete and dense time. Our model comprises automata with local timing constraints communicating over unbounded FIFO channels. Each automaton can only access its set of local clocks; all clocks evolve at the same rate. Our main contribution is a complete characterization of decidable and undecidable communication topologies, for both discrete and dense time. We also obtain complexity results, by showing that communicating timed processes are at least as hard as Petri nets; in the discrete time, we also show equivalence with Petri nets. Our results follow from mutual topology-preserving reductions between timed automata and (untimed) counter automata. To account for urgency of receptions, we also investigate the case where processes can test emptiness of channels.

References

  1. 1.
    Abdulla, P.A., Atig, M.F., Cederberg, J.: Timed lossy channel systems. In: FSTTCS. LIPIcs (2012)Google Scholar
  2. 2.
    Abdulla, P.A., Atig, M.F., Stenman, J.: Dense-timed pushdown automata. In: LICS, pp. 35–44 (2012)Google Scholar
  3. 3.
    Abdulla, P.A., Jonsson, B.: Verifying programs with unreliable channels. Information and Computation 127(2), 91–101 (1996)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Abdulla, P.A., Nylén, A.: Timed Petri Nets and BQOs. In: Colom, J.-M., Koutny, M. (eds.) ICATPN 2001. LNCS, vol. 2075, pp. 53–70. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Abdulla, P.A., Delzanno, G., Rezine, O., Sangnier, A., Traverso, R.: On the Verification of Timed Ad Hoc Networks. In: Fahrenberg, U., Tripakis, S. (eds.) FORMATS 2011. LNCS, vol. 6919, pp. 256–270. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  6. 6.
    Akshay, S., Bollig, B., Gastin, P.: Automata and Logics for Timed Message Sequence Charts. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 290–302. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Akshay, S., Bollig, B., Gastin, P., Mukund, M., Narayan Kumar, K.: Distributed Timed Automata with Independently Evolving Clocks. In: van Breugel, F., Chechik, M. (eds.) CONCUR 2008. LNCS, vol. 5201, pp. 82–97. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  8. 8.
    Akshay, S., Gastin, P., Mukund, M., Kumar, K.N.: Model checking time-constrained scenario-based specifications. In: FSTTCS. LIPIcs, vol. 8, pp. 204–215 (2010)Google Scholar
  9. 9.
    Alur, R., Dill, D.: A theory of timed automata. TCS 126(2), 183–235 (1994)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Bérard, B., Cassez, F., Haddad, S., Lime, D., Roux, O.H.: Comparison of Different Semantics for Time Petri Nets. In: Peled, D.A., Tsay, Y.-K. (eds.) ATVA 2005. LNCS, vol. 3707, pp. 293–307. Springer, Heidelberg (2005), http://dx.doi.org/10.1007/11562948_/23 CrossRefGoogle Scholar
  11. 11.
    Bonnet, R.: The Reachability Problem for Vector Addition System with One Zero-Test. In: Murlak, F., Sankowski, P. (eds.) MFCS 2011. LNCS, vol. 6907, pp. 145–157. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. 12.
    Brand, D., Zafiropulo, P.: On communicating finite-state machines. J. ACM 30(2), 323–342 (1983)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Cécé, G., Finkel, A.: Verification of programs with half-duplex communication. Information and Computation 202(2), 166–190 (2005)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Chambart, P., Schnoebelen, P.: Mixing Lossy and Perfect Fifo Channels. In: van Breugel, F., Chechik, M. (eds.) CONCUR 2008. LNCS, vol. 5201, pp. 340–355. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  15. 15.
    Chandrasekaran, P., Mukund, M.: Matching Scenarios with Timing Constraints. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 98–112. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Delzanno, G., Sangnier, A., Zavattaro, G.: Parameterized Verification of Ad Hoc Networks. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 313–327. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  17. 17.
    Gruber, H., Holzer, M., Kiehn, A., König, B.: On Timed Automata with Discrete Time – Structural and Language Theoretical Characterization. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 272–283. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  18. 18.
    Heußner, A., Leroux, J., Muscholl, A., Sutre, G.: Reachability analysis of communicating pushdown systems. Logical Methods in Comp. Sci. 8(3:23), 1–20 (2012)Google Scholar
  19. 19.
    Ibarra, O.H., Dang, Z., Pietro, P.S.: Verification in loosely synchronous queue-connected discrete timed automata. Theor. Comput. Sci. 290(3), 1713–1735 (2003)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Krcal, P., Yi, W.: Communicating Timed Automata: The More Synchronous, the More Difficult to Verify. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 249–262. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  21. 21.
    La Torre, S., Madhusudan, P., Parlato, G.: Context-Bounded Analysis of Concurrent Queue Systems. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 299–314. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  22. 22.
    Lipton, R.J.: The Reachability Problem Requires Exponential Space. Department of Computer Science, Yale University (1976)Google Scholar
  23. 23.
    Pachl, J.K.: Reachability problems for communicating finite state machines. Research Report CS-82-12, University of Waterloo (May 1982)Google Scholar
  24. 24.
    Reinhardt, K.: Reachability in petri nets with inhibitor arcs. ENTCS 223, 239–264 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Lorenzo Clemente
    • 1
  • Frédéric Herbreteau
    • 1
  • Amelie Stainer
    • 2
  • Grégoire Sutre
    • 1
  1. 1.CNRS, LaBRI, UMR 5800Univ. BordeauxTalenceFrance
  2. 2.University of Rennes 1RennesFrance

Personalised recommendations