On Presburger Liveness of Discrete Timed Automata

  • Zhe Dang
  • Pierluigi San Pietro
  • Richard A. Kemmerer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2010)

Abstract

Using an automata-theoretic approach, we investigate the decidability of liveness properties (called Presburger liveness properties) for timed automata when Presburger formulas on configurations are allowed. While the general problem of checking a temporal logic such as TPTL augmented with Presburger clock constraints is undecidable, we show that there are various classes of Presburger liveness properties which are decidable for discrete timed automata. For instance, it is decid- able, given a discrete timed automaton A and a Presburger property P, whether there exists an ω-path of A where P holds infinitely often. We also show that other classes of Presburger liveness properties are indeed undecidable for discrete timed automata, e.g., whether P holds infinitely often for each ω-path of A. These results might give insights into the cor- responding problems for timed automata over dense domains, and help in the definition of a fragment of linear temporal logic, augmented with Presburger conditions on configurations, which is decidable for model checking timed automata.

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References

  1. 1.
    R. Alur, “Timed automata”, CAV’99, LNCS 1633, pp. 8–22Google Scholar
  2. 2.
    R. Alur, C. Courcoubetis, and D. Dill, “Model-checking in dense real time,” Information and Computation, 104 (1993) 2–34MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    R. Alur and D. Dill, “Automata for modeling real-time systems,” Theoretical Computer Science, 126 (1994) 183–236MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    R. Alur, T. Feder, and T. A. Henzinger, “The benefits of relaxing punctuality,” J. ACM, 43 (1996) 116–146MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    R. Alur, T. A. Henzinger, “Real-time logics: complexity and expressiveness,” Information and Computation, 104 (1993) 35–77MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    R. Alur, T. A. Henzinger, “A really temporal logic,” J. ACM, 41 (1994) 181–204MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    A. Coen-Porisini, C. Ghezzi and R. Kemmerer, “Specification of real-time systems using ASTRAL,” IEEE Transactions on Software Engineering, 23 (1997) 572–598CrossRefGoogle Scholar
  8. 8.
    H. Comon and V. Cortier, “Flatness is not a weakness,” Proc. Computer Science Logic, 2000.Google Scholar
  9. 9.
    H. Comon and Y. Jurski, “Timed automata and the theory of real numbers,” CONCUR’99, LNCS 1664, pp. 242–257Google Scholar
  10. 10.
    Z. Dang, O. H. Ibarra, T. Bultan, R. A. Kemmerer, and J. Su, “Binary reachability analysis of discrete pushdown timed automata,” CAV’00, LNCS 1855, pp. 69–84Google Scholar
  11. 11.
    T. A. Henzinger, Z. Manna, and A. Pnueli, “What good are digital clocks?,” ICALP’92, LNCS 623, pp. 545–558Google Scholar
  12. 12.
    T. A. Henzinger and Pei-Hsin Ho, “HyTech: the Cornell hybrid technology tool,” Hybrid Systems II, LNCS 999, pp. 265–294Google Scholar
  13. 13.
    T. A. Henzinger, X. Nicollin, J. Sifakis, and S. Yovine, “Symbolic model checking for real-time systems,” Information and Computation, 111 (1994) 193–244MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    K. G. Larsen, P. Pattersson, and W. Yi, “UPPAAL in a nutshell,” International Journal on Software Tools for Technology Transfer, 1 (1997): 134–152MATHCrossRefGoogle Scholar
  15. 15.
    F. Laroussinie, K. G. Larsen, and C. Weise, “From timed automata to logic-and back,” MFCS’95, LNCS 969, pp. 529–539Google Scholar
  16. 16.
    F. Wang, “Parametric timing analysis for real-time systems,” Information and Computation, 130 (1996): 131–150MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    S. Yovine, “A verification tool for real-time systems,” International Journal on Software Tools for Technology Transfer, 1 (1997): 123–133MATHCrossRefGoogle Scholar
  18. 18.
    S. Yovine, “Model checking timed automata,” Embedded Systems’98, LNCS 1494, pp. 114–152Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Zhe Dang
    • 1
  • Pierluigi San Pietro
    • 2
  • Richard A. Kemmerer
    • 3
  1. 1.School of Electrical Engineering and Computer ScienceWashington State UniversityPullmanUSA
  2. 2.Dipartimento di Elettronica e InformazionePolitecnico di MilanoItalia
  3. 3.Department of Computer ScienceUniversity of California at Santa BarbaraUSA

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