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It therefore follows that, for any inner state sk , the clock constraint φsk , which holds upon 7 Formally, such an enumeration can be obtained by topologically sorting the underlying transition DAG. Undecidability of Universality for Timed Automata 35 entering sk , in fact holds continuously until the next transition occurs, unless that transition is headed for the sink state. A second important observation is that, once φsink holds, it holds forever. Indeed, the clock ev is never reset in the sink state, so the clock constraint ev ≥ 1, once true, never changes.
In: Proceedings of RTSS 03, IEEE Computer Society Press, Los Alamitos (2003) 13. : Using Mappings to Prove Timing Properties. Distributed Computing 6(2), 121–139 (1992) 14. : Recursive Unsolvability of Post’s Problem of “Tag” and Other Topics in the Theory of Turing Machines. Annals of Mathematics 74(3), 437–455 (1961) 15. : Digitisation and Full Abstraction for Dense-Time Model Checking. , Stevens, P. ) ETAPS 2002 and TACAS 2002. LNCS, vol. 2280, pp. 37–51. Springer, Heidelberg (2002) 16. : Revisiting Digitization, Robustness, and Decidability for Timed Automata.
Springer, Heidelberg (1996) 22. : Folk Theorems on the Determinization and Minimization of Timed Automata. , Niebert, P. ) FORMATS 2003. LNCS, vol. 2791, pp. 182–188. Springer, Heidelberg (2004) On Timed Models of Gene Networks Gr´egory Batt, Ramzi Ben Salah, and Oded Maler V ERIMAG, 2, av. fr Abstract. We present a systematic translation from timed models of genetic regulatory networks into products of timed automata to which one can apply verification tools in order learn about the possible qualitative behaviors of the network under a whole range of uncertain delay parameters.