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Untangling the Graphs of Timed Automata to Decrease the Number of Clocks

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Integrated Formal Methods (IFM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13274))

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Abstract

For timed automata, the question of whether the number of clocks can be decreased without violating the semantics is known to be undecidable. It is, however, possible to obtain a number of clocks that is optimal, in a well-defined sense, for a timed automaton with a given graph and set of constraints. Such an optimal allocation of clocks can be improved further by changing the automaton’s graph or its set of constraints. We address the first kind of change, and develop a novel method that may allow us to convert the automaton to one that requires fewer clocks, without changing its semantics.

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Notes

  1. 1.

    This is a common-sense condition of a strictly technical nature. In the literature it is often assumed that all the clocks are implicitly reset to zero before the initial location: we would accommodate that by adding a sequence of extra epsilon transitions before the initial location, each such transition annotated by a reset.

  2. 2.

    If there is no path from a location l to a final location, then l can be removed without affecting the language of the automaton.

  3. 3.

    In the sense of language equivalence.

  4. 4.

    An outline of the proof, too long to include here, is available from the authors.

References

  1. Abdulla, P.A., Deneux, J., Ouaknine, J., Worrell, J.: Decidability and complexity results for timed automata via channel machines. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1089–1101. Springer, Heidelberg (2005). https://doi.org/10.1007/11523468_88

    Chapter  MATH  Google Scholar 

  2. Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)

    Article  MathSciNet  Google Scholar 

  3. Alur, R., Madhusudan, P.: Decision problems for timed automata: a survey. In: Bernardo, M., Corradini, F. (eds.) SFM-RT 2004. LNCS, vol. 3185, pp. 1–24. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30080-9_1

    Chapter  MATH  Google Scholar 

  4. 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). https://doi.org/10.1007/978-3-642-02930-1_4

    Chapter  MATH  Google Scholar 

  5. Behrmann, G., Bouyer, P., Fleury, E., Larsen, K.G.: Static guard analysis in timed automata verification. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 254–270. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36577-X_18

    Chapter  MATH  Google Scholar 

  6. Bengtsson, J., Larsen, K., Larsson, F., Pettersson, P., Yi, W.: UPPAAL—a tool suite for automatic verification of real-time systems. In: Alur, R., Henzinger, T.A., Sontag, E.D. (eds.) HS 1995. LNCS, vol. 1066, pp. 232–243. Springer, Heidelberg (1996). https://doi.org/10.1007/BFb0020949

    Chapter  Google Scholar 

  7. Clarke, E.M., Jr., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (1999)

    MATH  Google Scholar 

  8. Daws, C., Tripakis, S.: Model checking of real-time reachability properties using abstractions. In: Steffen, B. (ed.) TACAS 1998. LNCS, vol. 1384, pp. 313–329. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0054180

    Chapter  Google Scholar 

  9. Daws, C., Yovine, S.: Reducing the number of clock variables of timed automata. In: Proceedings of the 17th IEEE Real-Time Systems Symposium (RTSS ’96), December 4–6, 1996, Washington, DC, USA. pp. 73–81 (1996)). https://doi.org/10.1007/978-3-642-33365-1_12

  10. Finkel, O.: Undecidable Problems About Timed Automata. CoRR abs/0712.1363 (2007)

    Google Scholar 

  11. Guha, S., Narayan, C., Arun-Kumar, S.: Reducing clocks in timed automata while preserving Bisimulation. In: Baldan, P., Gorla, D. (eds.) CONCUR 2014. LNCS, vol. 8704, pp. 527–543. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44584-6_36

    Chapter  Google Scholar 

  12. Saeedloei, N., Kluźniak, F.: Clock allocation in timed automata and graph colouring. In: Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week), HSCC 2018, Porto, Portugal, 11–13 April 2018, pp. 71–80 (2018). http://doi.acm.org/10.1145/3178126.3178138

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Authors and Affiliations

  1. Towson University, Towson, USA

    Neda Saeedloei

  2. LogicBlox, Atlanta, USA

    Feliks Kluźniak

Authors
  1. Neda Saeedloei
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  2. Feliks Kluźniak
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Correspondence to Neda Saeedloei .

Editor information

Editors and Affiliations

  1. ISTI-CNR, Pisa, Italy

    Maurice H. ter Beek

  2. Maynooth University, Maynooth, Ireland

    Rosemary Monahan

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Saeedloei, N., Kluźniak, F. (2022). Untangling the Graphs of Timed Automata to Decrease the Number of Clocks. In: ter Beek, M.H., Monahan, R. (eds) Integrated Formal Methods. IFM 2022. Lecture Notes in Computer Science, vol 13274. Springer, Cham. https://doi.org/10.1007/978-3-031-07727-2_10

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  • DOI: https://doi.org/10.1007/978-3-031-07727-2_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-07726-5

  • Online ISBN: 978-3-031-07727-2

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