On the Relationship between Reachability Problems in Timed and Counter Automata

  • Christoph Haase
  • Joël Ouaknine
  • James Worrell
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7550)


This paper establishes a relationship between reachability problems in timed automata and space-bounded counter automata. We show that reachability in timed automata with three or more clocks is naturally logarithmic-space interreducible with reachability in space-bounded counter automata with two counters. We moreover show the logarithmic-space equivalence of reachability in two-clock timed automata and space-bounded one-counter automata. This last reduction provides new insight into two problems whose precise computational complexity have independently been identified as open.


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  1. 1.
    Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comp. Sci. 126, 183–235 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Alur, R., Henzinger, T.A., Vardi, M.Y.: Parametric real-time reasoning. In: Proc. STOC, pp. 592–601. ACM Press (1993)Google Scholar
  3. 3.
    Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N., Srba, J.: Infinite Runs in Weighted Timed Automata with Energy Constraints. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 33–47. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Courcoubetis, C., Yannakakis, M.: Minimum and maximum delay problems in real-time systems. Form. Method. Syst. Des. 1(4), 385–415 (1992)zbMATHCrossRefGoogle Scholar
  5. 5.
    Figueira, D., Hofman, P., Lasota, S.: Relating timed and register automata. In: Proc. EXPRESS. EPTCS, vol. 41, pp. 61–75 (2010)Google Scholar
  6. 6.
    Haase, C., Kreutzer, S., Ouaknine, J., Worrell, J.: Reachability in Succinct and Parametric One-Counter Automata. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 369–383. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Laroussinie, F., Markey, N., Schnoebelen, P.: Model Checking Timed Automata with One or Two Clocks. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 387–401. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Memmi, G., Roucairol, G.: Linear Algebra in Net Theory. In: Brauer, W. (ed.) Net Theory and Applications. LNCS, vol. 84, pp. 213–223. Springer, Heidelberg (1980)CrossRefGoogle Scholar
  9. 9.
    Minsky, M.L.: Recursive unsolvability of post’s problem of ”tag” and other topics in theory of turing machines. Ann. Math. 74(3), 437–455 (1961)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Naves, G.: Accessibilité dans les automates temporisés à deux horloges. Rapport de Master, MPRI, Paris, France (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Christoph Haase
    • 1
  • Joël Ouaknine
    • 1
  • James Worrell
    • 1
  1. 1.Department of Computer ScienceUniversity of OxfordUK

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