Skip to main content

Computing behavioural relations, logically

  • Specification And Verification (Session 3)
  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 510))

Included in the following conference series:

Abstract

This paper develops a model-checking algorithm for a fragment of the modal mu-calculus and shows how it may be applied to the efficient computation of behavioral relations between processes. The algorithm's complexity is proportional to the product of the size of the process and the size of the formula, and thus improves on the best existing algorithm for such a fixed point logic. The method for computing preorders that the model checker induces is also more efficient than known algorithms.

Research supported by National Science Foundation/DARPA Grant CCR-9014775

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arnold, A., and P. Crubille. “A Linear Algorithm To Solve Fixed-Point Equations on Transition Systems.” Information Processing Letters, v. 29, 30 September 1988, pp. 57–66.

    Google Scholar 

  2. Boudol, G., de Simone, R. and Vergamini, D. “Experiment with Auto and Autograph on a Simple Case Sliding Window Protocol.” INRIA Report 870, July 1988.

    Google Scholar 

  3. Clarke, E.M., E.A. Emerson and Sistla, A.P. “Automatic Verification of Finite State Concurrent Systems Using Temporal Logic Specifications.” ACM Transactions on Programming Languages and Systems, v. 8, n. 2, 1986, pp. 244–263.

    Google Scholar 

  4. Cleaveland, R. “Tableau-Based Model Checking in the Propositional Mu-Calculus.” Acta Informatica, 1990.

    Google Scholar 

  5. Cleaveland, R. and Hennessy, M.C.B. “Testing Equivalence as a Bisimulation Equivalence.” In Proceedings of the Workshop on Automatic Verification Methods for Finite-State Systems. Lecture Notes in Computer Science series 407, Springer-Verlag, Berlin, 1989.

    Google Scholar 

  6. Cleaveland, R., Parrow, J. and Steffen, B. “The Concurrency Workbench.” In Proceedings of the Workshop on Automatic Verification Methods for Finite-State Systems, 1989, Lecture Notes in Computer Science 407, pp. 24–37. Springer-Verlag, Berlin.

    Google Scholar 

  7. Cleaveland, R., Parrow, J. and B. Steffen. A Semantics based Verification Tool for Finite State Systems, In pro. of the Ninth International Symposium on Protocol Specification, Testing, and Verification; North Holland, 1989.

    Google Scholar 

  8. Cleaveland, R. and Steffen, B. “When is ‘Partial’ Complete? A Logic-Based Proof Technique using Partial Specifications.” In Proceedings LICS'90, 1990.

    Google Scholar 

  9. DeNicola, R. and Hennessy, M.C.B. “Testing Equivalences for Processes.” Theoretical Computer Science 24, 1984, pp. 83–113.

    Google Scholar 

  10. Emerson, E.A. and Lei, C.-L. “Efficient Model Checking in Fragments of the Propositional Mu-Calculus.” In Proceedings of the First Annual Symposium on Logic in Computer Science, 1986, pp. 267–278.

    Google Scholar 

  11. Fernandez, J.-C. Aldébaran: Une Système de Vérification par Réduction de Processus Communicants. Ph.D. Thesis, Université de Grenoble, 1988.

    Google Scholar 

  12. Graf, S. and Steffen, B. “Using Interface Specifications for Compositional Reduction.” To appear in Proceedings of the Workshop on Computer-Aided Verification.

    Google Scholar 

  13. Kozen, D. “Results on the Propositional μ-Calculus.” Theoretical Computer Science, v. 27, 1983, pp. 333–354.

    Google Scholar 

  14. Larsen, K.G. “Proof Systems for Hennessy-Milner Logic with Recursion.” In Proceedings of CAAP, 1988.

    Google Scholar 

  15. Malhotra, J., Smolka, S.A., Giacalone, A. and Shapiro, R. “Winston: A Tool for Hierarchical Design and Simulation of Concurrent Systems.” In Proceedings of the Workshop on Specification and Verification of Concurrent Systems, University of Stirling, Scotland, 1988.

    Google Scholar 

  16. Milner, R. A Calculus of Communicating Systems. Lecture Notes in Computer Science 92. Springer-Verlag, Berlin, 1980.

    Google Scholar 

  17. Milner, R. Communication and Concurrency, Prentice Hall, 1989.

    Google Scholar 

  18. Plotkin, G. and Stirling, C. “A Framework for Intuitionistic Modal Logics.” Theoretical Aspects of Reasoning about Knowledge, Monterey, 1986.

    Google Scholar 

  19. Richier, J., Rodriguez, C., Sifakis, J. and Voiron, J. “Verification in XESAR of the Sliding Window Protocol.” In Proceedings of the Seventh IFIP Symposium on Protocol Specification, Testing, and Verification, 1987, North-Holland.

    Google Scholar 

  20. Steffen, B.U. “Characteristic Formulae for CCS with Divergence.” In Proceedings ICALP, Lecture Notes in Computer Science 372, pp. 723–733. Springer-Verlag, Berlin, 1989.

    Google Scholar 

  21. Steffen, B.U., and Ingólfsdóttir, A. “Characteristic Formulae for CCS with Divergence.” To appear in Theoretical Computer Science.

    Google Scholar 

  22. Stirling, C. “Modal Logics for Communicating Systems.” Theoretical Computer Science, v. 49, 1987, pp. 311–347.

    Google Scholar 

  23. Stirling, C., and Walker, D. “Local Model Checking in the Modal Mu-Calculus.” In Proceedings CAAP'89, Lecture Notes in Computer Science 351, pp. 369–383, 1989.

    Google Scholar 

  24. Tarski, A. “A Lattice-Theoretical Fixpoint Theorem and its Applications.” Pacific Journal of Mathematics, v. 5, 1955.

    Google Scholar 

  25. Walker, D. “Bisimulations and Divergence.” In Proceedings of the Third Annual Symposium on Logic in Computer Science, 1988, pp. 186–192. Computer Society Press, Washington DC.

    Google Scholar 

  26. Winskel, G. “On the Compositional Checking of Validity.” In Proceedings CONCUR'90, Lecture Notes in Computer Science 458, pp. 481–501, 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Javier Leach Albert Burkhard Monien Mario Rodríguez Artalejo

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cleaveland, R., Steffen, B. (1991). Computing behavioural relations, logically. In: Albert, J.L., Monien, B., Artalejo, M.R. (eds) Automata, Languages and Programming. ICALP 1991. Lecture Notes in Computer Science, vol 510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54233-7_129

Download citation

  • DOI: https://doi.org/10.1007/3-540-54233-7_129

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54233-9

  • Online ISBN: 978-3-540-47516-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics