Skip to main content
SpringerLink
Log in

Model-checking discrete duration calculus

  • Published:
Formal Aspects of Computing

Abstract

Duration Calculus was introduced in [ZHR91] as a logic to specify and reason about requirements for real-time systems. It is an extension of Interval Temporal Logic [Mos85] where one can reason about integrated constraints over time-dependent and Boolean valued states without explicit mention of absolute time. Several major case studies, e.g. the gas burner system in [RRH93], have shown that Duration Calculus provides a high level of abstraction for both expressing and reasoning about specifications. Using Timed Automata [A1D92] one can express how real-time systems can be constructed at a level of detail which is close to an actual implementation. We consider in the paper the correctness of Timed Automata with respect to Duration Calculus formulae. For a subset of Duration Calculus, we show that one can automatically verify whether a Timed Automaton ℳ is correct with respect to a formulaD, abbreviated ℳ ⊨D, i.e. one can domodel-checking. The subset we consider is expressive enough to formalize the requirements to the gas burner system given in [RRH93]; but only for a discrete time domain. Model-checking is done by reducing the correctness problem ℳ ⊨D to the inclusion problem of regular languages.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alur R., Courcoubetis C. and Dill D.: Model-Checking for Real-Time Systems. InFifth Annual IEEE Symp. on Logic in Computer Science, 1990, pp. 414–425.

  2. Alur R. and Dill D.: The Theory of Timed Automata. InReal-Time: Theory in Practice, J.W. de Bakker, C. Huizing, W.P. de Roever and G. Rozenberg (eds), LNCS 600, Springer-Verlag 1992, pp. 45–73.

  3. Alur R., Courcoubetis C, Henzinger T. and Ho P-H.: Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems. InHybrid Systems, R.L. Grossman, A. Nerode, A.P. Ravn and H. Rischel (eds), LNCS 736, Springer-Verlag 1993, pp. 209–229.

  4. Back R.J.R.: Refinement Calculus, Part II: Parallel and Reactive Programs. InStepwise Refinements of Distributed Systems: Models, Formalisms, Correctness, J.W. de Bakker, W.-P. de Roever and G. Rozenberg (eds), LNCS 430, Springer-Verlag 1990, pp. 67–93.

  5. Bauer R.:Model-checking for Duration Calculus, Oldenburg University, May 1993. (In German).

  6. Bouajjani A., Echahed R. and Robbana R.:Verifying Invariance Properties of Timed Systems with Duration Variables, Report from VERIMAG-SPECTRE, Miniparc-Zirst, Rue Lavoisier, 38330 Montbonnot St-Martin, France, 1994.

  7. Bouajjani A., Echahed R. and Sifakis J.: On Model Checking for Real-Time Properties with Durations. InEigth Annual IEEE Symp. on Logic in Computer Science, 1993, pp. 147–159.

  8. Bowen J., Olderog E.-R., Fränzle M. and Ravn A.P.: Developing Correct Systems. InProc. Fifth Euromicro Workshop on Real-Time Systems, IEEE Computer Society Press 1993, pp. 176–187.

  9. Clarke, E.M., Emerson, E.A. and Sistla, A.P.: Automatic Verification of Finite State Concurrent Systems using Temporal Logic.ACM Trans. on Programming Languages and Systems, 8(2), 244–263, (1986).

    Article  MATH  Google Scholar 

  10. Engel M., Kubica M., Madey J., Parnas D.L., Ravn A.P. and Schouwen AJ. van: A Formal Approach to Computer Systems Requirements Documentation. InHybrid Systems, R.L. Grossman, A. Nerode, A.P. Ravn and H. Rischel (eds), LNCS 736, Springer-Verlag 1993, pp. 252–474.

  11. Halpern J., Moszkowski B. and Manna Z.: A Hardware Semantics Based on Temporal Intervals. InICALP'83, J. Diaz (ed), LNCS 154, Springer-Verlag 1983, pp. 278–291.

  12. Hansen M.R. and Zhou Chaochen: Semantics and Completeness of Duration Calculus. InReal-Time: Theory in Practice, J. W. de Bakker, C. Huizing, W.-P. de Roever and G. Rozenberg (eds), LNCS 600, Springer-Verlag 1992, pp. 209–225.

  13. Hansen M.R. and Olderog E.-R.:Constructing Circuits from Decidable Duration Calculus, Oldenburg University, April 1993.

  14. Kesten Y., Pnueli A., Sifakis J. and Yovine S.: Integration Graphs: A Class of Decidable Hybrid Systems. InHybrid Systems, R.L. Grossman, A. Nerode, A.P. Ravn and H. Rischel (eds), LNCS 736, Springer-Verlag 1993, pp. 179–208.

  15. Koymans, R.: Specifying real-time properties with metric temporal logic.Real-Time Systems, 2(4), 255–299, (1990).

    Article  Google Scholar 

  16. Masiero P.C., Ravn A.P. and Rischel H.:Refinement of Real-Time Specifications. ProCoS II ESPRIT BRA 7071 report no. ID/DTH PCM 1/1, Department of Computer Science, Technical University of Denmark, 1993.

  17. Morgan C.:Programming from Specifications, Prentice Hall International, 1990.

  18. Moszkowski, B.: A Temporal Logic for Multilevel Reasoning about Hardware.IEEE Computer, 18(2), 10–19, 1985.

    Article  Google Scholar 

  19. Nicollin X., Sifakis J. and Yovine S.: From ATP to Timed Graphs and Hybrid Systems. InReal-Time: Theory in Practice, J. W. de Bakker, C. Huizing, W.-P. de Roever and G. Rozenberg (eds), LNCS 600, Springer-Verlag 1992, pp. 549–572.

  20. Olderog E.-R.:Nets, Terms and Formulas: Three Views of Concurrent Processes and Their Relationship, Cambridge University Press, 1991.

  21. Owre S, Shankar N. and Rushby J.M.:User Guide for the PVS Specification and Verification System, Language, and Proof Checker (Beta Release). Computer Science Laboratory, SRI International report (three volumes), Menlo Park, CA 94025, USA, 1993.

  22. Ramakrishna Y.S., Dillon L.K., Moser L.E., Melliar-Smith P.M. and Kutty G.: A Real-Time Interval Logic and Its Decision Procedure. InProc. Foundations of Software Technology and Theoretical Computer Science, R.K. Shyamasundar (ed), LNCS 761, Springer-Verlag, 1993, pp. 173–192.

  23. Ravn, A.P., Rischel, H. and Hansen, K.M.: Specifying and Verifying Requirements of Real-Time Systems.IEEE Trans. Softw. Eng., 19(1), 41–55, (1993).

    Article  Google Scholar 

  24. Rosner R. and Pnueli A.: A Choppy Logic. InProc. First Annual IEEE Symp. on Logic in Computer Science, 1986, pp. 306–313.

  25. Skakkebæk J.U.: Private communications, April 1993.

  26. Skakkebæk J.U. and Sestoft P.:Checking Validity of Duration Calculus Formulas. ProCoS II, ESPRIT BRA 7071, report no. ID/DTH JUS 3/1, Department of Computer Science, Technical University of Denmark, 1994.

  27. Skakkebæk, J.U. and Shankar, N.:A Duration Calculus Proof Checker: Using PVS as a Semantic Framework. Report no. SRI-CSL-93-10, Computer Science Laboratory, SRI International, Menlo Park, CA 94025, USA 1993.

    Google Scholar 

  28. Skakkebæk J.U., Ravn A.P., Rischel H. and Zhou Chaochen: Specification of Embedded, Real-Time Systems. InProc. Fourth Euromicro Workshop on Real-Time Systems, IEEE Computer Society Press 1992, pp. 116–121.

  29. Zhou Chaochen, Hansen M.R. and Sestoft P.: Decidability and Undecidability Results for Duration Calculus. InSTACS'93, P. Enjalbert, A. Finkel and K.W. Wagner (eds) LNCS 665, Springer-Verlag 1993, pp. 58–68.

  30. Zhou, Chaochen, Hoare, C.A.R. and Ravn, A.P.: A Calculus of Durations. InInformation Processing Letters, 40(5), 269–276, (1991).

    Article  MATH  MathSciNet  Google Scholar 

  31. Zhou Chaochen, Zhang Jingzhong, Yang Lu and Li Xiaoshan:Linear Duration Invariants. UNU/IIST Report no. 11, UNU/IIST, P.O. Box 3058, Macau, 1993.

  32. Zhou Chaochen and Li Xiaoshan: A Mean Value Calculus of Durations. InA Classical Mind: Essays in Honour of C.A.R. Hoare, A.W. Roscoe (ed), Prentice Hall International 1994, pp. 431–451.

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Technical University of Denmark, Building 344, DK-2800, Lyngby, Denmark

    Michael R. Hansen

Authors
  1. Michael R. Hansen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael R. Hansen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hansen, M.R. Model-checking discrete duration calculus. Formal Aspects of Computing 6 (Suppl 1), 826–845 (1994). https://doi.org/10.1007/BF01213605

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01213605

Keywords

Search

Navigation