Abstract
Time constraints are usually used in timed systems to rule on discrete behaviours based on the valuations of clocks. They are categorized into diagonal-free constraints and diagonal constraints. In timed automata, it is well-known that diagonal constraints are just a useful syntax sugar since each diagonal constraint can be encoded into diagonal-free constraints. However, it is yet unknown when recursion is taken into consideration. This paper investigates the decidability results of these systems with diagonal constraints, under the model of nested timed automata (NeTAs). We show that the NeTAs containing a singleton global clock with diagonal constraints are Turing complete, even when the clock assignment is restricted to the clock reset. In comparison, the reachability problem for a subclass, NeTAs without frozen clocks, is decidable under diagonal constraints.
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References
Mattai, J.: Real-Time Systems: Specification, Verification, and Analysis. Prentice Hall, Englewood Cliffs (1995)
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
Clemente, L., Lasota, S.: Timed pushdown automata, revisited. In: Proceedings of LICS 2015, pp. 738–749
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
Fang, B., Li, G., Sun, D., Cai, H.: Schedulability analysis of timed regular tasks by under-approximation on WCET. In: Fränzle, M., Kapur, D., Zhan, N. (eds.) SETTA 2016. LNCS, vol. 9984, pp. 147–162. Springer, Cham (2016). doi:10.1007/978-3-319-47677-3_10
Berard, B., Haddad, S., Sassolas, M.: Real time properties for interrupt timed automata. In: Proceedings of TIME 2010, pp. 69–76. IEEE Computer Society (2010)
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
Minsky, M.: Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)
Ouaknine, J., Worrell, J.: On the language inclusion problem for timed automata: closing a decidability gap. In: Proceedings of LICS 2004, pp. 54–63. IEEE Computer Society (2004)
Abdulla, P.A., Jonsson, B.: Verifying networks of timed processes. In: Steffen, B. (ed.) TACAS 1998. LNCS, vol. 1384, pp. 298–312. Springer, Heidelberg (1998). doi:10.1007/BFb0054179
Abdulla, P., Jonsson, B.: Model checking of systems with many identical time processes. Theoret. Comput. Sci. 290, 241–264 (2003)
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 LICS 2012, pp. 35–44. IEEE Computer Society (2012)
Abdulla, P.A., Atig, M.F., Stenman, J.: The minimal cost reachability problem in priced timed pushdown systems. In: Dediu, A.-H., MartÃn-Vide, C. (eds.) LATA 2012. LNCS, vol. 7183, pp. 58–69. Springer, Heidelberg (2012). doi:10.1007/978-3-642-28332-1_6
Alur, R., Etessami, K., Yannakakis, M.: Analysis of recursive state machines. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 207–220. Springer, Heidelberg (2001). doi:10.1007/3-540-44585-4_18
Benerecetti, M., Minopoli, S., Peron, A.: Analysis of timed recursive state machines, pp. 61–68. In: Proceedings of the TIME 2010. IEEE Computer Society (2010)
Wang, Y., Li, G., Yuen, S.: Nested timed automata with various clocks. Sci. Found. Chin. 24, 51–68 (2016)
Tian, C., Duan, Z.: Detecting spurious counterexamples efficiently in abstract model checking. In: Proceedings of the ICSE 2013, pp. 202–211. IEEE/ACM (2013)
Tian, C., Duan, Z., Duan, Z.: Making CEGAR more efficient in software model checking. IEEE Trans. Softw. Eng. 40, 1206–1223 (2014)
Liu, Y., Duan, Z., Tian, C.: A decision procedure for a fragment of linear time Mu-calculus. In: Proceedings of the IJCAI 2016, pp. 1195–1201. IJCAI/AAAI Press (2016)
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This work is supported by National Natural Science Foundation of China with grant No. 61472240, 61672340, 61472238, and the NSFC-JSPS bilateral joint research project with grant No. 61511140100.
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Wang, Y., Wen, Y., Li, G., Yuen, S. (2017). Nested Timed Automata with Diagonal Constraints. In: Duan, Z., Ong, L. (eds) Formal Methods and Software Engineering. ICFEM 2017. Lecture Notes in Computer Science(), vol 10610. Springer, Cham. https://doi.org/10.1007/978-3-319-68690-5_24
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DOI: https://doi.org/10.1007/978-3-319-68690-5_24
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