On Reachability Analysis of Updatable Timed Automata with One Updatable Clock
As an extension of Timed Automata (TAs), Updatable Timed Automata (UTAs) proposed by Bouyer et al. have the ability to update clocks in a more elaborate way than simply reset them to zero. The reachability of general UTAs is undecidable, by regarding a pair of updatable clocks as counters updatable with incrementation and decrementation operations. This paper investigates the model of subclass of UTAs by restricting the number of updateable clocks. It is shown that the reachability of UTAs with one updatable clock (UTA1s) under diagonal-free constraints is decidable. The decidability is proved by treating a region of a UTA1 as an unbounded digiword, and encoding sets of digiwords that are accepted by a pushdown system where regions are generated on-the-fly on the stack.
This work is supported by the NSFC-JSPS bilateral joint research project (61511140100), the National Natural Science Foundation of China (No. 61472240, 91318301, 61261130589), and JSPS KAKENHI Grant-in-Aid for Scientific Research(B) (15H02684, 25280023) and Challenging Exploratory Research (26540026).
- 5.Schwoon, S.: Model-checking pushdown system. Ph.D. thesis, Technical University of Munich (2000)Google Scholar
- 6.Ouaknine, J., Worrell, J.: On the language inclusion problem for timed automata: closing a decidability gap. In: Proceedings of the 19th IEEE Symposium on Logic in Computer Science (LICS’04), IEEE Computer Society, pp. 54–63 (2004)Google Scholar
- 14.Wen, Y., Li, G., Yuen, S.: An over-approximation forward analysis for nested timed automata. In: Liu, S., Duan, Z. (eds.) SOFL+MSVL 2014. LNCS, vol. 8979, pp. 62–80. Springer, Heidelberg (2015)Google Scholar
- 17.Fang, B., Li, G., Fang, L., Xiang, J.: A refined algorithm for reachability analysis of updatable timed automata. In: Proceedings of the 1st IEEE International Workshop on Software Engineering and Knowledge Management (SEKM 2015 @ QRS 2015), IEEE Computer Society, pp. 230–236 (2015)Google Scholar