Adding Dense-Timed Stack to Integer Reset Timed Automata

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10506)

Abstract

Integer reset timed automata (IRTA) are known to be a determinizable subclass of timed automata, but it is not known whether they are input-determined, i.e., the clock values are completely determined by an input timed word. We first define a syntactic subclass of IRTA called strict IRTA and show that strict IRTA is equivalent to IRTA. We show that the class of strict IRTA is indeed input-determined. Visibly pushdown automata is another input-determined class of automata with a stack that is also closed under boolean operations and admits a logical characterization. We propose dtIRVPA as a class of timed automata with a dense-timed stack. Similar to strict IRTA, we define strict dtIRVPA and show that strict dtIRVPA is input-determined where both – stack operations and the values of the integer reset clocks – are determined by the input word, and this helps us to get the monadic second-order (MSO) logical characterization of dtIRVPA. We prove the closure properties of dtIRVPA under union, intersection, complementation, and determinization. Further, we show that reachability of dtIRVPA is PSPACE-complete, i.e. the complexity is no more than that of timed automata.

Keywords

Visibly pushdown automata Dense-timed stack Integer reset timed automata Logical characterization MSO 

References

  1. 1.
    Abdulla, P.A., Atig, M.F., Stenman, J.: Dense-timed pushdown automata. In: LICS, pp. 35–44 (2012)Google Scholar
  2. 2.
    Aceto, L., Laroussinie, F.: Is your model checker on time? on the complexity of model checking for timed modal logics. J. Log. Algebr. Program. 52–53, 7–51 (2002)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Akshay, S., Gastin, P., Krishna, S.N.: Analyzing timed systems using tree automata. In: CONCUR, pp. 27:1–27:14 (2016)Google Scholar
  4. 4.
    Alur, R., Dill, D.: A theory of timed automata. Theor. Comput. Sci. 126, 183–235 (1994)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Alur, R., Madhusudan, P.: Visibly pushdown languages. In: STOC, pp. 202–211 (2004)Google Scholar
  6. 6.
    Baier, C., Bertrand, N., Bouyer, P., Brihaye, T.: When are timed automata determinizable? In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 43–54. Springer, Heidelberg (2009). doi:10.1007/978-3-642-02930-1_4 CrossRefGoogle Scholar
  7. 7.
    Bhave, D., Dave, V., Krishna, S.N., Phawade, R., Trivedi, A.: A logical characterization for dense-time visibly pushdown automata. In: Dediu, A.-H., Janoušek, J., Martín-Vide, C., Truthe, B. (eds.) LATA 2016. LNCS, vol. 9618, pp. 89–101. Springer, Cham (2016). doi:10.1007/978-3-319-30000-9_7 CrossRefGoogle Scholar
  8. 8.
    Bhave, D., Dave, V., Krishna, S.N., Phawade, R., Trivedi, A.: A perfect class of context-sensitive timed languages. In: Brlek, S., Reutenauer, C. (eds.) DLT 2016. LNCS, vol. 9840, pp. 38–50. Springer, Heidelberg (2016). doi:10.1007/978-3-662-53132-7_4 CrossRefGoogle Scholar
  9. 9.
    Bouajjani, A., Echahed, R., Robbana, R.: On the automatic verification of systems with continuous variables and unbounded discrete data structures. Hybrid Syst. II, 64–85 (1995)MathSciNetGoogle Scholar
  10. 10.
    Clemente, L., Lasota, S.: Timed pushdown automata revisited. In: LICS, pp. 738–749 (2015)Google Scholar
  11. 11.
    Dang, Z.: Binary reachability analysis of pushdown timed automata with dense clocks. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 506–517. Springer, Heidelberg (2001). doi:10.1007/3-540-44585-4_48 CrossRefGoogle Scholar
  12. 12.
    Droste, M., Perevoshchikov, V.: A logical characterization of timed pushdown languages. In: Beklemishev, L.D., Musatov, D.V. (eds.) CSR 2015. LNCS, vol. 9139, pp. 189–203. Springer, Cham (2015). doi:10.1007/978-3-319-20297-6_13 Google Scholar
  13. 13.
    D’Souza, D., Tabareau, N.: On timed automata with input-determined guards. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS/FTRTFT -2004. LNCS, vol. 3253, pp. 68–83. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30206-3_7 CrossRefGoogle Scholar
  14. 14.
    Henzinger, T.A., Majumdar, R., Prabhu, V.S.: Quantifying similarities between timed systems. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 226–241. Springer, Heidelberg (2005). doi:10.1007/11603009_18 CrossRefGoogle Scholar
  15. 15.
    Lautemann, C., Schwentick, T., Thérien, D.: Logics for context-free languages. In: Pacholski, L., Tiuryn, J. (eds.) CSL 1994. LNCS, vol. 933, pp. 205–216. Springer, Heidelberg (1995). doi:10.1007/BFb0022257 CrossRefGoogle Scholar
  16. 16.
    Li, G., Cai, X., Ogawa, M., Yuen, S.: Nested timed automata. In: Braberman, V., Fribourg, L. (eds.) FORMATS 2013. LNCS, vol. 8053, pp. 168–182. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40229-6_12 CrossRefGoogle Scholar
  17. 17.
    Li, G., Ogawa, M., Yuen, S.: Nested timed automata with frozen clocks. In: Sankaranarayanan, S., Vicario, E. (eds.) FORMATS 2015. LNCS, vol. 9268, pp. 189–205. Springer, Cham (2015). doi:10.1007/978-3-319-22975-1_13 CrossRefGoogle Scholar
  18. 18.
    Manasa, L., Krishna, S.N.: Integer reset timed automata: clock reduction and determinizability. CoRR, abs/1001.1215 (2010)Google Scholar
  19. 19.
    Mohalik, A., Rajeev, C., Dixit, M.G., Ramesh, S., Suman, P.V., Pandya, P.K., Jiang, S.: Model checking based analysis of end-to-end latency in embedded, real-time systems with clock drifts. In: DAC (2008)Google Scholar
  20. 20.
    Suman, P.V., Pandya, P.K., Krishna, S.N., Manasa, L.: Timed automata with integer resets: language inclusion and expressiveness. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 78–92. Springer, Heidelberg (2008). doi:10.1007/978-3-540-85778-5_7 CrossRefGoogle Scholar
  21. 21.
    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). doi:10.1007/978-3-642-15643-4_23 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Indian Institute of Technology BombayMumbaiIndia
  2. 2.The Hebrew University of JerusalemJerusalemIsrael

Personalised recommendations