dCTL: A Branching Time Temporal Logic for Fault-Tolerant System Verification

  • Pablo F. Castro
  • Cecilia Kilmurray
  • Araceli Acosta
  • Nazareno Aguirre
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7041)


With the increasing demand for highly dependable and constantly available systems, being able to reason about faults and their impact on systems is gaining considerable attention. In this paper, we are concerned with the provision of a logic especially tailored for describing fault tolerance properties, and supporting automated verification. This logic, which we refer to as dCTL, employs temporal deontic operators in order to distinguish “good” (normal) from “bad” (faulty) behaviors, using deontic permission, prohibition and obligation combined in a novel way with temporal operators. These formulas are interpreted over transition systems, in which normal executions are distinguished from faulty ones. Furthermore, we show that this logic is sufficiently expressive to describe various common properties of interest in fault tolerant systems, and show that it features some desirable characteristics that make it suitable for analysis. Indeed, even though we show that the logic is more expressive than CTL, we prove that it maintains the time complexity of the model checking problem for CTL. The logic, its expressiveness and its use to express properties of fault tolerant systems, are illustrated via some case studies.


Formal Methods Fault Tolerance Temporal Logic Model Checking 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Arora, A., Gouda, M.: Closure and Convergence: A Foundation of Fault-Tolerant Computing. IEEE Transactions on Software Engineering 19(11) (1999)Google Scholar
  2. 2.
    Baier, C., Katoen, J.-P.: Principles of Model Checking. The MIT Press, Cambridge (2008)zbMATHGoogle Scholar
  3. 3.
    Castro, P., Maibaum, T.: Deontic Action Logic, Atomic Boolean Algebras and Fault-Tolerance. Journal of Applied Logic 7(4) (2009)Google Scholar
  4. 4.
    Clarke, E., Draghicescu, I.: Expressibility Results for Linear Time and Branching Time Logic. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency. LNCS, vol. 354, pp. 428–437. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  5. 5.
    Clarke, E., Emerson, E., Sistla, A.: Automatic Verification of Finite-State Concurrent Systems using Temporal Logic Specifications. ACM Transactions on Programming Languages and Systems 8(2) (1986)Google Scholar
  6. 6.
    Clarke, E., Grumberg, O., Peled, D.: Model Checking. The MIT Press, Cambridge (1999)Google Scholar
  7. 7.
    Coenen, J.: Specifying Fault Tolerant Programs in Deontic Logic, Computing Science Notes 91/34, Dept. of Mathematics and Computing Science, Eindhoven University of Technology, Eindhoven, The Netherlands (1991)Google Scholar
  8. 8.
    D’Ippolito, N., Braberman, V., Piterman, N., Uchitel, S.: Synthesis of Live Behaviour Models for Fallible Domains. In: Proc. of International Conference on Software Engineering ICSE 2011. IEEE Press, Los Alamitos (2011)Google Scholar
  9. 9.
    Emerson, E., Halpern, J.: “Sometimes” and “Not Never” revisited: on branching versus linear time temporal logic. J. ACM 33(1) (1986)Google Scholar
  10. 10.
    French, T., McCabe-Dansted, J., Reynolds, M.: A Temporal Logic of Robustness. In: Konev, B., Wolter, F. (eds.) FroCos 2007. LNCS (LNAI), vol. 4720, pp. 193–205. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Gnesi, E., Lenzini, G., Martinelli, F.: Logical Specification and Analysis of Fault Tolerant Systems through Partial Model Checking. Electronic Notes on Theoretical Computer Science, vol. 118. Elsevier, Amsterdam (2005)zbMATHGoogle Scholar
  12. 12.
    Janowski, T.: On Bisimulation, Fault-Monotonicity and Provable Fault-Tolerance. In: Johnson, M. (ed.) AMAST 1997. LNCS, vol. 1349, pp. 292–306. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  13. 13.
    Magee, J., Maibaum, T.: Towards Specification, Modelling and Analysis of Fault Tolerance in Self Managed Systems. In: Proc. of International Workshop on Self-Adaptation and Self-Managing Systems SEAMS 2006. ACM Press, New York (2006)Google Scholar
  14. 14.
    McCabe-Dansted, J., French, T., Reynolds, M., Pinchinat, S.: On the Expressivity of RoCTL*. In: Proc. of the 16th International Symposium on Temporal Representation and Reasoning TIME 2009. IEEE Computer Society, Los Alamitos (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Pablo F. Castro
    • 1
    • 3
  • Cecilia Kilmurray
    • 1
  • Araceli Acosta
    • 2
    • 3
  • Nazareno Aguirre
    • 1
    • 3
  1. 1.Departamento de Computación, FCEFQyNUniversidad Nacional de Río CuartoRío CuartoArgentina
  2. 2.Facultad de Matemática, Astronomía y FísicaUniversidad Nacional de CórdobaArgentina
  3. 3.Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)Argentina

Personalised recommendations