Abstract
Timed finite automata, introduced by Alur and Dill, are one of the most widely studied models for real-time systems. We focus in this paper on the power of silent transitions, i.e. ε-transitions, in such automata. We show that ε-transitions strictly increase the power of timed automata and that the class of timed languages recognized by automata with ε-transitions is much more robust than the corresponding class without ε-transitions. Our main result shows that these transitions increase the power of these automata only if they reset clocks.
Preview
Unable to display preview. Download preview PDF.
References
R. Alur, C. Courcoubetis, Dill D., N. Halbwachs, and H. Wong-Toi. Minimization of timed transition systems. In Proceedings of CONCUR'92, LNCS 630, 1992.
R. Alur, C. Courcoubetis, and T.A. Henzinger. The observational power of clocks. In Proceedings of CONCUR'94, LNCS 836, pages 162–177, 1994.
R. Alur and D.L. Dill. Automata for modeling real-time systems. In Proceedings of ICALP'90, LNCS 443, pages 322–335, 1990.
R. Alur and D.L. Dill. A theory of timed automata. Theoretical Computer Science, 126:183–235, 1994.
R. Alur, L. Fix, and T.A. Henzinger. A determinizable class of timed automata. In Proceedings of CAV'94, LNCS 818, pages 1–13, 1994.
R. Alur and T.A. Henzinger. Back to the future: towards a theory of timed regular languages. In Proceedings of FOCS'92, LNCS, pages 177–186, 1992.
B. Bérard. Untiming timed languages. Information Processing Letters, 55:129–135, 1995.
B. Bérard, P. Gastin, and A. Petit. On the power of non observable actions in timed automata. Tech. Rep. 95.08, ENS de Cachan, LIFAC, 1995.
E. Clarke, E.A. Emerson, and A.P. Sistla. Automatic verification of finite-state concurrent systems using temporal-logic specifications. ACM Trans. Programming Languages and Systems, 8:244–263, 1986.
C. Courcoubetis and M. Yannakakis. Minimum and maximum delay problems in real-time systems. In Proceedings of CAV'91, LNCS 575, pages 399–409, 1991.
T. Henzinger, Z. Manna, and A. Pnueli. Temporal proofs methodologies for realtime systems. In Proceedings of POPL '91, pages 353–366, 1991.
T. Henzinger, X. Nicollin, J. Sifakis, and S. Yovine. Symbolic model checking for real-time systems. Information und Computation, 111(2):193–244, 1994.
T.A. Henzinger, P.W. Kopke, and Wong Toi H., The expressive power of clocks. In Proceedings of ICALP'95, LNCS 944, pages 335–346, 1995.
N. Lynch and H. Attiya. Using mappings to prove timing properties. In Proceedings of PODC'90, pages 265–280, 1990.
X. Nicollin, J. Sifakis, and S. Yovine. From ATP to timed graphs and hybrid systems. In Proceedings of REX workshop ”Real-time: theory in practice”, LNCS 600, pages 549–572, 1991.
J. Ostroff. Temporal Logic of Real-time Systems. Research Studies Press, 1990.
C. Ramchandani. Analysis of asynchronous concurrent systems by petri nets. Technical report, Massachusetts Institute of Technology, 1974.
W. Thomas. Automata on infinite objects. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 133–191. Elsevier Science Publishers (North-Holland), 1990.
M. Vardi. Verification of concurrent-programs — the automata-theoretic framework. In Proceedings of LICS'87, pages 167–176, 1987.
P. Wolper, M. Vardi, and A.P. Sistla. Reasoning about infinite computation paths. In Proceedings of FOCS'83, pages 185–194, 1983.
H. Wong-Toi and G. Hoffmann. The control of dense real-time discrete event systems. In Proceedings of the 30th IEEE Conf. on Decision and Control, pages 1527–1528, 1991.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bérard, B., Gastin, P., Petit, A. (1996). On the power of non-observable actions in timed automata. In: Puech, C., Reischuk, R. (eds) STACS 96. STACS 1996. Lecture Notes in Computer Science, vol 1046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60922-9_22
Download citation
DOI: https://doi.org/10.1007/3-540-60922-9_22
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60922-3
Online ISBN: 978-3-540-49723-3
eBook Packages: Springer Book Archive