Skip to main content
SpringerLink
Log in

Computable CTL * for Discrete-Time and Continuous-Space Dynamic Systems

  • Conference paper
Book cover Reachability Problems (RP 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5797))

Included in the following conference series:

Abstract

The CTL * model-checking problem is thoroughly studied and is fully understood for finite and countable state spaces. Yet, in most models arising in the sciences and engineering the system’s sate space is uncountable. Then, the standard computability and complexity theory is inapplicable but the semantics of CTL * has to be in some sense computable to allow for model-checking algorithms that are implementable on digital computers. To tackle this problem, we consider discrete-time continuous-space dynamic systems for which we study the computability of the standard semantics of CTL * and provide a variant thereof computable in the sense of Type-2 Theory of Effectivity.

This research was supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) Vidi grant 639.032.408.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Artemov, S.N., Davoren, J.M., Nerode, A.: Logic, Topological Semantics and Hybrid Systems. In: International Conference on Decision and Control, CDC 1997, vol. 1, pp. 698–701. IEEE Press, Los Alamitos (1997)

    Google Scholar 

  2. Balluchi, A., Casagrande, A., Collins, P., Ferrari, A., Villa, T., Sangiovanni-Vincentelli, A.L.: Ariadne: A Framework for Reachability Analysis of Hybrid Automata. In: Symposium on Mathematical Theory of Networks and Systems (MTNS 2006), Kyoto, Japan (July 2006) (to appear)

    Google Scholar 

  3. Brattka, V., Presser, G.: Computability on subsets of metric spaces. Theoretical Computer Science 305(1-3), 43–76 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications. AMC Transactions On Programming Languages And Systems 8(2), 244–263 (1986)

    Article  MATH  Google Scholar 

  5. Clarke, E.M., Draghicescu, I.A.: Expressibility Results for Linear-Time and Branching-Time Logics. In: Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, School/Workshop, London, UK, pp. 428–437. Springer, Heidelberg (1989)

    Chapter  Google Scholar 

  6. Collins, P.: Continuity and computability of reachable sets. Theoretical Computer Science 341(1), 162–195 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Collins, P.: Optimal Semicomputable Approximations to Reachable and Invariant Sets. Theory of Computing Systems 41(1), 33–48 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Collins, P.J., Zapreev, I.S.: Computable CTL for Discrete-Time and Continuous-Space Dynamic Systems. Technical Report MAS-E0903, MAS, Centrum Wiskunde & Informatica (2009), http://www.cwi.nl/ftp/CWIreports/MAS/MAS-E0903.pdf

  9. Collins, P.J., Zapreev, I.S.: Computable CTL for Discrete-Time and Continuous-Space Dynamic Systems. In: Computability in Europe, CiE (2009), To be published in a local pre-conference proceedings volume

    Google Scholar 

  10. Emerson, E.A., Halpern, J.Y.: “sometimes” and “Not Never” Revisited: On Branching versus Linear Time Temporal Logic. Journal of the Association for Computing Machinery (ACM) 33(1), 151–178 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kozen, D.: Results on the propositional μ-calculus. Research Report RC 10133 (44981), IBM Research Division, August 1983, p. 42 (1983)

    Google Scholar 

  12. Kremer, P., Mints, G.: Dynamic topological logic. Annals of Pure and Applied Logic 131(1–3), 133–158 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kupferman, O., Vardi, M.Y.: From Linear Time to Branching Time. ACM Transactions on Computational Logic (TOCL) 6(2), 273–294 (2005)

    Article  MathSciNet  Google Scholar 

  14. Maidl, M.: The Common Fragment of CTL and LTL. In: Annual Symposium on Foundations of Computer Science, FOCS 2000, pp. 643–652. IEEE Computer Society, Los Alamitos (2000)

    Google Scholar 

  15. Nerode, A., Kohn, W.: Models for Hybrid Systems: Automata, Topologies, Controllability, Observability. In: Grossman, R.L., Ravn, A.P., Rischel, H., Nerode, A. (eds.) HS 1991 and HS 1992. LNCS, vol. 736, pp. 317–356. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  16. Pnueli, A.: The Temporal Semantics of Concurrent Programs. In: Kahn, G. (ed.) Semantics of Concurrent Computation. LNCS, vol. 70, pp. 1–20. Springer, Heidelberg (1979)

    Chapter  Google Scholar 

  17. Schneider, K.: Verification of Reactive Systems: Formal Methods and Algorithms. In: TTCSS. Springer, Heidelberg (2004)

    Google Scholar 

  18. Schnoebelen, P.: The complexity of temporal logic model checking. In: Balbiani, P., Suzuki, N.-Y., Wolter, F., Zakharyaschev, M. (eds.) Selected Papers from the 4th Workshop on Advances in Modal Logics (AiML), Toulouse, France, pp. 393–436. King’s College Publication (2003)

    Google Scholar 

  19. Spreen, D.: On the Continuity of Effective Multifunctions. Electron. Notes Theor. Comput. Sci. 221, 271–286 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  20. Weihrauch, K.: Computable Analysis: An Introduction. Springer, New York (2000)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centrum Wiskunde & Informatica, Science Park 123, 1098, XG, Amsterdam

    Pieter Collins & Ivan S. Zapreev

Authors
  1. Pieter Collins
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ivan S. Zapreev
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Ecole Polytechnique, Laboratoire d’ Informatique (LIX), 91128, Palaiseau Cedex, France

    Olivier Bournez

  2. Department of Computer Science, Ashton Building, University of Liverpool, L69 3BX, Liverpool, England

    Igor Potapov

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Collins, P., Zapreev, I.S. (2009). Computable CTL * for Discrete-Time and Continuous-Space Dynamic Systems. In: Bournez, O., Potapov, I. (eds) Reachability Problems. RP 2009. Lecture Notes in Computer Science, vol 5797. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04420-5_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-04420-5_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04419-9

  • Online ISBN: 978-3-642-04420-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation