Abstract
Timed systems can be considered with two types of semantics – dense time semantics and discrete time semantics. The most typical examples of both of them are real semantics and sampled semantics (i.e., discrete semantics with a fixed time step ε). We investigate the relations between real semantics and sampled semantics with respect to different behavioral equivalences. Also, we study decidability of reachability problem for stopwatch automata with sampled semantics. Finally, our main technical contribution is decidability of non-emptiness of a timed automaton ω-language in some sampled semantics (this problem was previously wrongly classified as undecidable). For the proof we employ a novel characterization of reachability relations between configurations of a timed automaton.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)
Alur, R., Madhusudan, P.: Decision problems for timed automata: A survey. In: Bernardo, M., Corradini, F. (eds.) SFM-RT 2004. LNCS, vol. 3185, pp. 1–24. Springer, Heidelberg (2004)
Asarin, E., Maler, O., Pnueli, A.: On discretization of delays in timed automata and digital circuits. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 470–484. Springer, Heidelberg (1998)
Bouyer, P., Dufourd, C., Fleury, E., Petit, A.: Are timed automata updatable? In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 464–479. Springer, Heidelberg (2000)
Bozga, M., Maler, O., Pnueli, A., Yovine, S.: Some Progress in the Symbolic Verification of Timed Automata. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 179–190. Springer, Heidelberg (1997)
Bozga, M., Maler, O., Tripakis, S.: Efficient verification of timed automata using dense and discrete time semantics. In: Pierre, L., Kropf, T. (eds.) CHARME 1999. LNCS, vol. 1703, pp. 125–141. Springer, Heidelberg (1999)
Cassez, F., Henzinger, T.A., Raskin, J.-F.: A comparison of control problems for timed and hybrid systems. In: Tomlin, C.J., Greenstreet, M.R. (eds.) HSCC 2002. LNCS, vol. 2289, pp. 134–148. Springer, Heidelberg (2002)
Comon, H., Jurski, Y.: Timed automata and the theory of real numbers. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 242–257. Springer, Heidelberg (1999)
Dima, C.: Computing reachability relations in timed automata. In: Proc. of Symp. on Logic in Computer Science (LICS 2002), pp. 177–188. IEEE Computer Society Press, Los Alamitos (2002)
Gollu, A., Puri, A., Varaiya, P.: Discretization of timed automata. In: Proc. of Conferene on Decision and Control, pp. 957–958 (1994)
Grumberg, O., Lerda, F., Strichman, O., Theobald, M.: Proof-guided underapproximation-widening for multi-process systems. In: Proc. of Principles of programming languages (POPL 2005), pp. 122–131. ACM Press, New York (2005)
Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? In: Proc. of ACM Symposium on Theory of Computing (STOC 1995), pp. 373–382. ACM Press, New York (1995)
Henzinger, T.A., Manna, Z., Pnueli, A.: What good are digital clocks? In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623, pp. 545–558. Springer, Heidelberg (1992)
Krčál, P., Pelánek, R.: Reachability relations and sampled semantics of timed systems. Technical Report FIMU-RS-2005-09, Masaryk University Brno (2005)
Larsen, K.G., Yi, W.: Time-abstracted bisimulation: Implicit specifications and decidability. Information and Computation 134(2), 75–101 (1997)
Ouaknine, J., Worrell, J.: Revisiting digitization, robustness, and decidability for timed automata. In: Proc. of IEEE Symp. on Logic in Computer Science (LICS 2003), pp. 198–207. IEEE Computer Society Press, Los Alamitos (2003)
Pasareanu, C., Pelánek, R., Visser, W.: Concrete search with abstract matching and refinement. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 52–66. Springer, Heidelberg (2005) (to appear)
Puri, A.: Dynamical properties of timed automata. Discrete Event Dynamic Systems 10(1-2), 87–113 (2000)
Stirling, C.: Local model checking games. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 1–11. Springer, Heidelberg (1995)
De Wulf, M., Doyen, L., Raskin, J.-F.: Almost ASAP semantics: From timed models to timed implementations. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 296–310. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Krčál, P., Pelánek, R. (2005). On Sampled Semantics of Timed Systems. In: Sarukkai, S., Sen, S. (eds) FSTTCS 2005: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2005. Lecture Notes in Computer Science, vol 3821. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11590156_25
Download citation
DOI: https://doi.org/10.1007/11590156_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30495-1
Online ISBN: 978-3-540-32419-5
eBook Packages: Computer ScienceComputer Science (R0)