skip to main content
research-article

Alternating timed automata

Published: 07 April 2008 Publication History

Abstract

A notion of alternating timed automata is proposed. It is shown that such automata with only one clock have decidable emptiness problem over finite words. This gives a new class of timed languages that is closed under boolean operations and which has an effective presentation. We prove that the complexity of the emptiness problem for alternating timed automata with one clock is nonprimitive recursive. The proof gives also the same lower bound for the universality problem for nondeterministic timed automata with one clock. We investigate extension of the model with epsilon-transitions and prove that emptiness is undecidable. Over infinite words, we show undecidability of the universality problem.

References

[1]
Abdulla, P. and Jonsson, B. 1998. Veryfying networks of timed processes. In Proceedings of the International Conference Tools and Algorithms for the Construction and Analysis of System (TACAS'98). Lecture Notes in Computer Science. Springer-Verlag, New York, 298--312.
[2]
Abdulla, P. and Jonsson, B. 2001. Timed petri nets and BQOs. In Proceedings of the ICATPN'01. 53--70.
[3]
Abdulla, P., Čer&abar;ns, K., Jonsson, B., and Tsay, Y. 1996. General decidability theorems for infinite state systems. In Proceedings of the IEEE Symposium on Logic in Computer Science (LICS'96). IEEE Computer Society Press, Los Alamitos, CA, 313--323.
[4]
Abdulla, P. A., Deneux, J., Ouaknine, J., and Worrell, J. 2005. Decidability and complexity results for timed automata via channel machines. In Proceedings of the International Colloquium on Automata, Language and Programming (ICALP'05). Lecture Notes in Computer Science, vol. 3580. Springer-Verlag, New York, 1089--1101.
[5]
Alur, R., Bernadsky, M., and Madhusudan, P. 2004. Optimal reachability for weighted timed games. In Proceedings of the International Colloquium on Automata, Languages and Programming (ICALP). Lecture Notes in Computer Science, vol. 3124. Springer-Verlag, New York, 122--133.
[6]
Alur, R. and Dill, D. 1994. A theory of timed automata. Theoret. Comput. Sci. 126, 183--235.
[7]
Alur, R., Fix, L., and Henzinger, T. 1999. Event-clock automata: A determinizable class of timed automata. Theoret. Comput. Sci. 204, 253--273.
[8]
Alur, R., Henzinger, T., and Vardi, M. 1993. Parametric real--time reasoning. In Proceedings of the Symposium on Theory of Computing (STOC'93). ACM, New York, 592--601.
[9]
Asarin, E., Maler, O., Pnueli, A., and Sifakis, J. 1998. Controller synthesis for timed automata. In Proceedings of the IFAC Symposium on System Structure and Control. 469--474.
[10]
Bérard, B., Diekert, V., Gastin, P., and Petit, A. 1998. Characterization of the expressive power of silent transitions in timed automata. Fund. Inf. 36, 2, 145--182.
[11]
Bouyer, P., Cassez, F., Fleury, E., and Larsen, K. G. 2004. Optimal strategies in priced timed game automata. In Proceedings of the FSTTCS'04. Lecture Notes in Computer Science, vol. 3328. Springer-Verlag, New York, 148--160.
[12]
Bouyer, P., D'Souza, D., Madhusudan, P., and Petit, A. 2003. Timed control with partial observability. In Proceedings of the CAV'03, Lecture Notes in Computer Science, vol. 2725. Springer-Verlag, 180--192.
[13]
Brand, D. and Zafiropulo, P. 1983. On communicating finite-state machines. J. ACM 30, 2, 323--342.
[14]
Cassez, F., Henzinger, T. A., and Raskin, J.-F. 2002. A comparison of control problems for timed and hybrid systems. In Proceedings of the Hybrid Systems Computation and Control (HSCC'02). 134--148.
[15]
Dickhöfer, M. and Wilke, T. 1999. Timed alternating tree automata: the automata-theoretic solution to the TCTL model checking problem. In Proceedings of the International Colloquium on Automata, Language and Programming (ICALP'99). Lecture Notes in Computer Science, vol. 1644. Springer-Verlag, New York, 281--290.
[16]
Dima, C. 2000. Real-time automata and the Kleene algebra of sets of real numbers. In Proceedings of the STACS'00. Lecture Notes in Computer Science, vol. 1170. Springer-Verlag, New York, 279--289.
[17]
Finkel, A. and Schnoebelen, P. 2001. Well structured transition systems everywhere! Theoret. Comput. Sci. 256, 1-2, 63--92.
[18]
Higman, G. 1952. Ordering by divisibility in abstract algebras. Proc. London Math. Soc. 2, 7, 326--336.
[19]
Laroussinie, F., Markey, N., and Schnoebelen, P. 2004. Model checking timed automata with one or two clocks. In Proceedings of the CONCUR'04. Lecture Notes in Computer Science, vol. 3170. Springer-Verlag, New York, 387--401.
[20]
Ouaknine, J. and Worrell, J. 2004. On the language inclusion problem for timed automata: Closing a decidability gap. In Proceedings of the IEEE Symposium on Logic in Computer Science (LICS'04). IEEE Computer Society Press, Los Alamitos, CA, 54--63.
[21]
Ouaknine, J. and Worrell, J. 2005. On the decidability of metric temporal logic. In Proceedings of the IEEE Symposium on Logic in Computer Science (LICS'05). IEEE Computer Society Press, Los Alamitos, CA, 188--197.
[22]
Schnoebelen, P. 2002. Verifying lossy channel systems has nonprimitive recursive complexity. Inf. Proc. Lett. 83, 5, 251--261.
[23]
Torre, S. L. and Napoli, M. 2001. Timed tree automata with an application to temporal logic. Acta Inf. 38, 2, 89--116.

Cited By

View all
  • (2025)Metric quantifiers and counting in timed logics and automataInformation and Computation10.1016/j.ic.2025.105268303(105268)Online publication date: Mar-2025
  • (2023)From Non-punctuality to Non-adjacency: A Quest for Decidability of Timed Temporal Logics with QuantifiersFormal Aspects of Computing10.1145/357174935:2(1-50)Online publication date: 23-Jun-2023
  • (2021)On the Modeling of Sequential Reactive Systems by Means of Real Time AutomataAutomatic Control and Computer Sciences10.3103/S014641162107017855:7(751-762)Online publication date: 1-Dec-2021
  • Show More Cited By

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Computational Logic
ACM Transactions on Computational Logic  Volume 9, Issue 2
March 2008
271 pages
ISSN:1529-3785
EISSN:1557-945X
DOI:10.1145/1342991
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 07 April 2008
Accepted: 01 September 2006
Revised: 01 August 2006
Received: 01 December 2005
Published in TOCL Volume 9, Issue 2

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. Alternation
  2. emptyness problem
  3. timed automata

Qualifiers

  • Research-article
  • Research
  • Refereed

Funding Sources

  • Polish government

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)23
  • Downloads (Last 6 weeks)0
Reflects downloads up to 15 Feb 2025

Other Metrics

Citations

Cited By

View all
  • (2025)Metric quantifiers and counting in timed logics and automataInformation and Computation10.1016/j.ic.2025.105268303(105268)Online publication date: Mar-2025
  • (2023)From Non-punctuality to Non-adjacency: A Quest for Decidability of Timed Temporal Logics with QuantifiersFormal Aspects of Computing10.1145/357174935:2(1-50)Online publication date: 23-Jun-2023
  • (2021)On the Modeling of Sequential Reactive Systems by Means of Real Time AutomataAutomatic Control and Computer Sciences10.3103/S014641162107017855:7(751-762)Online publication date: 1-Dec-2021
  • (2020)On the Modeling of Sequential Reactive Systems by Means of Real Time AutomataModeling and Analysis of Information Systems10.18255/1818-1015-2020-4-396-41127:4(396-411)Online publication date: 20-Dec-2020
  • (2018)Model Checking Real-Time SystemsHandbook of Model Checking10.1007/978-3-319-10575-8_29(1001-1046)Online publication date: 19-May-2018
  • (2016)Complexity Hierarchies beyond ElementaryACM Transactions on Computation Theory10.1145/28587848:1(1-36)Online publication date: 3-Feb-2016
  • (2015)Real-Time Languages, Timed Alternating Automata, and Timed Temporal Logics: Relationships and SpecificationsProcedia Computer Science10.1016/j.procs.2015.08.40962(47-54)Online publication date: 2015
  • (2015)Generalized Post Embedding ProblemsTheory of Computing Systems10.1007/s00224-014-9561-956:4(697-716)Online publication date: 1-May-2015
  • (2014)Relating timed and register automataMathematical Structures in Computer Science10.1017/S096012951400032226:06(993-1021)Online publication date: 5-Dec-2014
  • (2013)A survey of timed automata for the development of real-time systemsComputer Science Review10.1016/j.cosrev.2013.05.0019(1-26)Online publication date: Aug-2013
  • Show More Cited By

View Options

Login options

Full Access

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media