Skip to main content

Nested Timed Automata with Invariants

  • Conference paper
  • First Online:
Dependable Software Engineering. Theories, Tools, and Applications (SETTA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10606))

  • 540 Accesses

Abstract

Invariants are usually adopted into timed systems to constrain the time passage within each control location. It is well-known that a timed automaton with invariants can be encoded to an equivalent one without invariants. When recursions are taken into consideration, few results show whether invariants affect expressiveness. This paper investigates the effect of invariants to Nested Timed Automata (NeTAs), a typical real-timed recursive system. In particular, we study the reachability problem for NeTA-Is, which extend NeTAs with invariants. It is shown that the reachability problem is undecidable on NeTA-Is with a single global clock, while it is decidable when no invariants are given. Furthermore, we also show that the reachability is decidable if the NeTA-Is contains no global clocks by showing that a good stack content still satisfies well-formed constraints.

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 EPUB and 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

Similar content being viewed by others

Notes

  1. 1.

    The NeTAs here are called “NeTA-Fs” in [5].

References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Henzinger, T.A., Nicollin, X., Sifakis, J., Yovine, S.: Symbolic model checking for real-time systems. Inf. Comput. 111, 193–244 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bengtsson, J., Yi, W.: Timed automata: semantics, algorithms and tools. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) ACPN 2003. LNCS, vol. 3098, pp. 87–124. Springer, Heidelberg (2004). doi:10.1007/978-3-540-27755-2_3

    Chapter  Google Scholar 

  4. Li, G., Cai, X., Ogawa, M., Yuen, S.: Nested timed automata. In: Braberman, V., Fribourg, L. (eds.) FORMATS 2013. LNCS, vol. 8053, pp. 168–182. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40229-6_12

    Chapter  Google Scholar 

  5. Li, G., Ogawa, M., Yuen, S.: Nested timed automata with frozen clocks. In: Sankaranarayanan, S., Vicario, E. (eds.) FORMATS 2015. LNCS, vol. 9268, pp. 189–205. Springer, Cham (2015). doi:10.1007/978-3-319-22975-1_13

    Chapter  Google Scholar 

  6. Cai, X., Ogawa, M.: Well-structured pushdown system: case of dense timed pushdown automata. In: Codish, M., Sumii, E. (eds.) FLOPS 2014. LNCS, vol. 8475, pp. 336–352. Springer, Cham (2014). doi:10.1007/978-3-319-07151-0_21

    Chapter  Google Scholar 

  7. Abdulla, P.A., Atig, M.F., Stenman, J.: Dense-timed pushdown automata. In: Proceedings of the LICS 2012, pp. 35–44. IEEE Computer Society (2012)

    Google Scholar 

  8. Trivedi, A., Wojtczak, D.: Recursive timed automata. In: Bouajjani, A., Chin, W.-N. (eds.) ATVA 2010. LNCS, vol. 6252, pp. 306–324. Springer, Heidelberg (2010). doi:10.1007/978-3-642-15643-4_23

    Chapter  Google Scholar 

  9. Benerecetti, M., Minopoli, S., Peron, A.: Analysis of timed recursive state machines. In: Proceedings of the TIME 2010, pp. 61–68. IEEE Computer Society (2010)

    Google Scholar 

  10. Minsky, M.: Computation: Finite and Infinite Machines. Prentice-Hall, Upper Saddle River (1967)

    MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by National Natural Science Foundation of China with grant Nos. 61472240, 61672340, 61472238, and the NSFC-JSPS bilateral joint research project with grant No. 61511140100.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Guoqiang Li .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Wang, Y., Li, G., Yuen, S. (2017). Nested Timed Automata with Invariants. In: Larsen, K., Sokolsky, O., Wang, J. (eds) Dependable Software Engineering. Theories, Tools, and Applications. SETTA 2017. Lecture Notes in Computer Science(), vol 10606. Springer, Cham. https://doi.org/10.1007/978-3-319-69483-2_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-69483-2_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-69482-5

  • Online ISBN: 978-3-319-69483-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics