Advertisement

The Minimal Cost Reachability Problem in Priced Timed Pushdown Systems

  • Parosh Aziz Abdulla
  • Mohamed Faouzi Atig
  • Jari Stenman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7183)

Abstract

This paper introduces the model of priced timed pushdown systems as an extension of discrete-timed pushdown systems with a cost model that assigns multidimensional costs to both transitions and stack symbols. For this model, we consider the minimal cost reachability problem: i.e., given a priced timed pushdown system and a target set of configurations, determine the minimal possible cost of any run from the initial to a target configuration. We solve the problem by reducing it to the reachability problem in standard pushdown systems.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abdulla, P.A., Mayr, R.: Minimal Cost Reachability/Coverability in Priced Timed Petri Nets. In: de Alfaro, L. (ed.) FOSSACS 2009. LNCS, vol. 5504, pp. 348–363. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  2. 2.
    Abdulla, P.A., Mayr, R.: Computing optimal coverability costs in priced timed Petri nets. In: LICS 2011, pp. 399–408. IEEE Computer Society (2011)Google Scholar
  3. 3.
    Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Alur, R., La Torre, S., Pappas, G.J.: Optimal paths in weighted timed automata. Theor. Comput. Sci. 318(3), 297–322 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Benerecetti, M., Minopoli, S., Peron, A.: Analysis of timed recursive state machines. In: Markey, N., Wijsen, J. (eds.) TIME, pp. 61–68. IEEE Computer Society (2010)Google Scholar
  6. 6.
    Bouajjani, A., Echahed, R., Robbana, R.: On the Automatic Verification of Systems with Continuous Variables and Unbounded Discrete Data Structures. In: Antsaklis, P.J., Kohn, W., Nerode, A., Sastry, S.S. (eds.) HS 1994. LNCS, vol. 999, pp. 64–85. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  7. 7.
    Bouajjani, A., Esparza, J., Maler, O.: 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)CrossRefGoogle Scholar
  8. 8.
    Bouyer, P., Cassez, F., Fleury, E., Larsen, K.G.: Optimal Strategies in Priced Timed Game Automata. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 148–160. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Dang, Z., Ibarra, O., Bultan, T., Kemmerer, R., Su, J.: Binary Reachability Analysis of Discrete Pushdown Timed Automata. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 69–84. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  10. 10.
    Emmi, M., Majumdar, R.: Decision Problems for the Verification of Real-Time Software. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 200–211. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Esparza, J., Knoop, J.: An Automata-Theoretic Approach to Interprocedural Data-Flow Analysis. In: Thomas, W. (ed.) FOSSACS 1999. LNCS, vol. 1578, pp. 14–30. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  12. 12.
    Higman, G.: Ordering by divisibility in abstract algebras. Proc. London Math. Soc (3) 2(7), 326–336 (1952)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation, 3rd edn. Addison-Wesley Longman Publishing Co., Inc. (2006)Google Scholar
  14. 14.
    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
  15. 15.
    Valk, R., Jantzen, M.: The residue of vector sets with applications to decidability problems in Petri nets. Acta Inf. 21, 643–674 (1985)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Parosh Aziz Abdulla
    • 1
  • Mohamed Faouzi Atig
    • 1
  • Jari Stenman
    • 1
  1. 1.Uppsala UniversitySweden

Personalised recommendations