On Presburger Liveness of Discrete Timed Automata
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Using an automata-theoretic approach, we investigate the decidability of liveness properties (called Presburger liveness properties) for timed automata when Presburger formulas on configurations are allowed. While the general problem of checking a temporal logic such as TPTL augmented with Presburger clock constraints is undecidable, we show that there are various classes of Presburger liveness properties which are decidable for discrete timed automata. For instance, it is decid- able, given a discrete timed automaton A and a Presburger property P, whether there exists an ω-path of A where P holds infinitely often. We also show that other classes of Presburger liveness properties are indeed undecidable for discrete timed automata, e.g., whether P holds infinitely often for each ω-path of A. These results might give insights into the cor- responding problems for timed automata over dense domains, and help in the definition of a fragment of linear temporal logic, augmented with Presburger conditions on configurations, which is decidable for model checking timed automata.
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- 1.R. Alur, “Timed automata”, CAV’99, LNCS 1633, pp. 8–22Google Scholar
- 8.H. Comon and V. Cortier, “Flatness is not a weakness,” Proc. Computer Science Logic, 2000.Google Scholar
- 9.H. Comon and Y. Jurski, “Timed automata and the theory of real numbers,” CONCUR’99, LNCS 1664, pp. 242–257Google Scholar
- 10.Z. Dang, O. H. Ibarra, T. Bultan, R. A. Kemmerer, and J. Su, “Binary reachability analysis of discrete pushdown timed automata,” CAV’00, LNCS 1855, pp. 69–84Google Scholar
- 11.T. A. Henzinger, Z. Manna, and A. Pnueli, “What good are digital clocks?,” ICALP’92, LNCS 623, pp. 545–558Google Scholar
- 12.T. A. Henzinger and Pei-Hsin Ho, “HyTech: the Cornell hybrid technology tool,” Hybrid Systems II, LNCS 999, pp. 265–294Google Scholar
- 15.F. Laroussinie, K. G. Larsen, and C. Weise, “From timed automata to logic-and back,” MFCS’95, LNCS 969, pp. 529–539Google Scholar
- 18.S. Yovine, “Model checking timed automata,” Embedded Systems’98, LNCS 1494, pp. 114–152Google Scholar