Exact Incremental Analysis of Timed Automata with an SMT-Solver

  • Bahareh Badban
  • Martin Lange
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6919)


Timed automata as acceptors of languages of finite timed words form a very useful framework for the verification of safety properties of real-time systems. Many of the classical automata-theoretic decision problems are undecidable for timed automata, for instance the inclusion or the universality problem. In this paper we consider restrictions of these problems: universality for deterministic timed automata and inclusion of a nondeterministic one by a deterministic one. We then advocate the use of SMT solvers for the exact incremental analysis of timed automata via these problems. We stratify these problems by considering domains of timed words of bounded length only and show that each bounded instance is in (co-)NP. We present some experimental data obtained from a prototypical implementation measuring the practical feasibility of the approach to timed automata via SMT solvers.


Hamiltonian Path Predicate Logic Inclusion Problem Hybrid Automaton Time Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
  2. 2.
    Abdulla, P.A., Deneux, J., Ouaknine, J., Quaas, K., Worrell, J.: Universality Analysis for One-Clock Timed Automata. Fundamenta Informaticae, 89 (2008)Google Scholar
  3. 3.
    Alur, R., Dill, D.L.: A Theory of Timed Automata. Theo. Comp. Sci. (1994)Google Scholar
  4. 4.
    Alur, R., Madhusudan, P.: Decision Problems for Timed Automata: A Survey. In: SFM School (2004)Google Scholar
  5. 5.
    Audemard, G., Bozzano, M., Cimatti, A., Sebastiani, R.: Verifying industrial hybrid systems with mathsat. ENTCS 119(2) (2005)Google Scholar
  6. 6.
    Audemard, G., Cimatti, A., Kornilowicz, A., Sebastiani, R.: Bounded model checking for timed systems. In: Peled, D.A., Vardi, M.Y. (eds.) FORTE 2002. LNCS, vol. 2529, Springer, Heidelberg (2002)Google Scholar
  7. 7.
    Barrett, C., Stump, A., Tinelli, C.: The SMT-LIB Standard: Version 2.0. Technical report (2010),
  8. 8.
    Bérard, B., Petit, A., Diekert, V., Gastin, P.: Characterization of the expressive power of silent transitions in timed automata. Fundam. Inform. 36(2-3) (1998)Google Scholar
  9. 9.
    Bouyer, P.: Untameable timed automata! In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 620–631. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  10. 10.
    Bouyer, P., Laroussinie, F., Reynier, P.-A.: Diagonal constraints in timed automata: Forward analysis of timed systems. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 112–126. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Cook, S.A.: The complexity of theorem-proving procedures. In: 3rd Annual ACM Symposium on Theory of Computing (STOC), pp. 151–158 (1971)Google Scholar
  12. 12.
    de Moura, L.M., Rueß, H., Sorea, M.: Bounded model checking and induction: From refutation to verification (extended abstract, category a). In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 14–26. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Fränzle, M., Herde, C.: HySAT: An efficient proof engine for bounded model checking of hybrid systems. Formal Methods in System Design 30(3) (2007)Google Scholar
  14. 14.
    Henzinger, T.A., Manna, Z., Pnueli, A.: What good are digital clocks? In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623, Springer, Heidelberg (1992)Google Scholar
  15. 15.
    Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103 (1972)Google Scholar
  16. 16.
    Khachiyan, L.G.: A polynomial algorithm in linear programming. Doklady Akademiia Nauk SSSR, 224 (1979)Google Scholar
  17. 17.
    Niebert, P., Mahfoudh, M., Asarin, E., Bozga, M., Maler, O., Jain, N.: Verification of timed automata via satisfiability checking. In: Damm, W., Olderog, E.-R. (eds.) FTRTFT 2002. LNCS, vol. 2469, pp. 225–243. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  18. 18.
    Ouaknine, J., Worrell, J.: Revisiting digitization, robustness, and decidability for timed automata. In: LICS (2003)Google Scholar
  19. 19.
    Ouaknine, J., Worrell, J.: On the Language Inclusion Problem for Timed Automata: Closing a Decidability Gap. In: LICS (2004)Google Scholar
  20. 20.
    Strichman, O.: Pruning techniques for the SAT-based bounded model checking problem. In: Margaria, T., Melham, T.F. (eds.) CHARME 2001. LNCS, vol. 2144, pp. 58–70. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  21. 21.
    Zbrzezny, A.: SAT-based Reachability Checking for Timed Automata with Diagonal Constraints. Fundam. Inform. 67(1-3), 303–322 (2005)MathSciNetzbMATHGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Bahareh Badban
    • 1
  • Martin Lange
    • 1
  1. 1.School of Elect. Eng. and Computer ScienceUniversity of KasselGermany

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