Skip to main content

Bounded Determinization of Timed Automata with Silent Transitions

  • Conference paper
  • First Online:
Formal Modeling and Analysis of Timed Systems (FORMATS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9268))

Abstract

Deterministic timed automata are strictly less expressive than their non-deterministic counterparts, which are again less expressive than those with silent transitions. As a consequence, timed automata are in general non-determinizable. This is unfortunate since deterministic automata play a major role in model-based testing, observability and implementability. However, by bounding the length of the traces in the automaton, effective determinization becomes possible. We propose a novel procedure for bounded determinization of timed automata. The procedure unfolds the automata to bounded trees, removes all silent transitions and determinizes via disjunction of guards. The proposed algorithms are optimized to the bounded setting and thus are more efficient and can handle a larger class of timed automata than the general algorithms. The approach is implemented in a prototype tool and evaluated on several examples. To our best knowledge, this is the first implementation of this type of procedure for timed automata.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bernhard, K.: Aichernig and florian lorber. Towards generation of adaptive test cases from partial models of determinized timed automata. In: AMOST (2015)

    Google Scholar 

  2. Aichernig, B.K., Lorber, F., Ničković, D.: Time for mutants — model-based mutation testing with timed automata. In: Veanes, M., Viganò, L. (eds.) TAP 2013. LNCS, vol. 7942, pp. 20–38. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

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

    Article  MathSciNet  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, Part II. LNCS, vol. 5556, pp. 43–54. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  5. Bérard, B., Petit, A., Diekert, V., Gastin, P.: Characterization of the expressive power of silent transitions in timed automata. Fundam. Inform. 36(2–3), 145–182 (1998)

    MATH  Google Scholar 

  6. Bertrand, N., Jéron, T., Stainer, A., Krichen, M.: Off-line test selection with test purposes for non-deterministic timed automata. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 96–111. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  7. Bertrand, N., Stainer, A., Jéron, T., Krichen, M.: A game approach to determinize timed automata. In: Hofmann, M. (ed.) FOSSACS 2011. LNCS, vol. 6604, pp. 245–259. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  8. Biere, A., Cimatti, A., Clarke, E.M., Strichman, O., Zhu, Y.: Bounded model checking. Advances in Computers 58, 117–148 (2003)

    Article  Google Scholar 

  9. 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)

    Chapter  Google Scholar 

  10. de Moura, L., Bjørner, N.S.: Z3: An efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. Diekert, V., Gastin, P., Petit, A.: Removing epsilon-transitions in timed automata. In: STACS, pp. 583–594. Springer (1997)

    Google Scholar 

  12. Finkel, O.: Undecidable problems about timed automata. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 187–199. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  13. Krichen, M., Tripakis, S.: Conformance testing for real-time systems. Formal Methods in System Design 34(3), 238–304 (2009)

    Article  MATH  Google Scholar 

  14. Larsen, K.G., Pettersson, P., Yi, W.: Uppaal in a nutshell. STTT 1(1–2), 134–152 (1997)

    Article  MATH  Google Scholar 

  15. Lorber, F., Rosenmann, A., Ničković, D., Aichernig, B.K.: Bounded determinization of timed automata with silent transitions. Technical Report IST-MBT-2015-01. Graz University of Technology, Institute for Software Technology (2015). https://goo.gl/YTjjnF

  16. Tretmans, Jan: Test generation with inputs, outputs, and quiescence. In: Margaria, Tiziana, Steffen, Bernhard (eds.) TACAS 1996. LNCS, vol. 1055, pp. 127–146. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  17. Tripakis, S.: Folk theorems on the determinization and minimization of timed automata. Inf. Process. Lett. 99(6), 222–226 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. Wang, T., Sun, J., Liu, Y., Wang, X., Li, S.: Are timed automata bad for a specification language? language inclusion checking for timed automata. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014 (ETAPS). LNCS, vol. 8413, pp. 310–325. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Florian Lorber .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Lorber, F., Rosenmann, A., Ničković, D., Aichernig, B.K. (2015). Bounded Determinization of Timed Automata with Silent Transitions. In: Sankaranarayanan, S., Vicario, E. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2015. Lecture Notes in Computer Science(), vol 9268. Springer, Cham. https://doi.org/10.1007/978-3-319-22975-1_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-22975-1_19

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22974-4

  • Online ISBN: 978-3-319-22975-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics