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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
The NeTAs here are called “NeTA-Fs” in [5].
References
Alur, R., Dill, D.L.: A theory of timed automata. Theoret. Comput. Sci. 126, 183–235 (1994)
Henzinger, T.A., Nicollin, X., Sifakis, J., Yovine, S.: Symbolic model checking for real-time systems. Inf. Comput. 111, 193–244 (1994)
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
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
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
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
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)
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
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)
Minsky, M.: Computation: Finite and Infinite Machines. Prentice-Hall, Upper Saddle River (1967)
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
Corresponding author
Editor information
Editors and Affiliations
Rights 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)