Skip to main content

Abstract interpretation and verification of reactive systems

  • Conference paper
  • First Online:
  • 132 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 724))

Abstract

This paper presents a variant of a refined partition algorithm, which exploits the irrelevance of unreachable states. When the state space is infinite, the number of accessible classes may be finite and the number of inaccessible classes infinite. The underlying idea is to incorporate a reachability analysis based on the concept of abstract interpretation. The new algorithm may terminate in cases where the original algorithm diverges.

This work was partially supported by ESPRIT Basic Research Action “SPEC”

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Bouajjani, S. Bensalem, C. Loiseaux, and J. Sifakis. Property preserving simulations. In Workshop on Computer-Aided Verification (CAV), Montréal, page, To appear LNCS, June 1992.

    Google Scholar 

  2. J.R. Burch, E.M. Clarke, K.L McMillan, D.L. Dill, and J. Hwang. Symbolic model checking: 1020 states and beyond. In Proc. 5th IEEE,LICS, 1990.

    Google Scholar 

  3. A. Bouali and R. de Simone. Symbolic bisimulation minimisation. In Fourth Workshop on Computer-Aided Verification,Montreal, june 1992.

    Google Scholar 

  4. A. Bouajjani, J.C. Fernandez, and N. Halbwachs. Minimal model generation. In Workshop on Computer-aided Verification, Rutgers, American Mathematical Society, Association for Computing Machinery, June 1990.

    Google Scholar 

  5. A. Bouajjani, J.C. Fernandez, N. Halbwachs, C. Ratel, and P. Raymond. Minimal state graph generation. Science of Computer Programming, 18(3), June 1992.

    Google Scholar 

  6. R. E. Bryant. Graph-based algorithms for boolean function manipulation. IEEE Transactions on Computers, C-35(8), 1986.

    Google Scholar 

  7. O. Coudert, C. Berthet, and J. C. Madre. Verification of synchronous sequential machines based on symbolic execution. In International Workshop on Automatic Verification Methods for Finite State Systems, LNCS 407, Springer Verlag, 1989.

    Google Scholar 

  8. P. Cousot and R. Cousot. Static determination of dynamic properties of programs. In 2th Int. Symp. on Programming, pages 106, 130, Dunod, 1976.

    Google Scholar 

  9. P. Cousot and R. Cousot. Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In 4th POPL, January 1977.

    Google Scholar 

  10. P. Cousot and R. Cousot. Comparing the Galois Connectionn and Widening/Narrowing Approaches to Abstract Interpretation. Technical Report, LIX, Ecole Polytechnique, May 1990.

    Google Scholar 

  11. P. Cousot and N. Halbwachs. Automatic discovery of linear restraints among variables of a program. In 5th. Annual Symp. on Principles of Programming Languages, pages 84–87, 1977.

    Google Scholar 

  12. P. Cousot. Semantic Foundations of Program Analysis, chapter 10. Prentice Hall, Inc., Englewood Cliffs, 1981.

    Google Scholar 

  13. R. Enders, T. Filkorn, and D. Taubner. Generating bdds for symbolic model checking in ccs. In K. G. Larsen, editor, Proceedings of the 3rd Workshop on Computer-Aided Verification (Aalborg, Denmark), july 1–4 1991.

    Google Scholar 

  14. J. C. Fernandez. An implementation of an efficient algorithm for bisimulation equivalence. Science of Computer Programming, 13(2–3), May 1990.

    Google Scholar 

  15. J. Cl. Fernandez, A. Kerbrat, and L. Mounier. Symbolic equivalence checking. In Workshop on Computer-aided Verification, University of Crete, to appear, July 1993.

    Google Scholar 

  16. J.Cl. Fernandez and L. Mounier. A tool set for deciding behavioural equivalences. In J.F. Groote J.C.M. Baeten, editor, CONCUR'91, Concurrency theory, LNCS 527, Springer Verlag, August 26–29 1991.

    Google Scholar 

  17. R.J. Van Glabbeek and W.P. Weijland. Branching time and abstraction in bisimulation semantics (extended abstract). CS-R 8911, Centrum voor Wiskunde en Informatica, Amsterdam, 1989.

    Google Scholar 

  18. N. Halbwachs. Détermination Automatique de Relations Linéaires Vérifiées par les Variables d'un Programme. PhD thesis, Université de Grenoble, 1979.

    Google Scholar 

  19. N. Halbwachs, P. Raymond, and C. Ratel. Generating efficient code from dataflow programs. In Third International Symposium on Programming Language Implementation and Logic Programming, Passau, August 1991.

    Google Scholar 

  20. P. Kanellakis and S. Smolka. Ccs expressions, finite state processes and three problems of equivalence. Information and Computation, 86(1), May 1990.

    Google Scholar 

  21. R. Milner. A calculus of communication systems. In LNCS 92, Springer Verlag, 1980.

    Google Scholar 

  22. D. Park. Concurrency and automata on infinite sequences. In 5th GI-Conference on Theorical Computer Science, Springer Verlag, 1981. LNCS 104.

    Google Scholar 

  23. Luis E. Sanchis. Data types as lattices: retractions, projection and projection. In RAIRO Theorical computer science, vol 11, nr 4, pages 339–344, 1977.

    Google Scholar 

  24. J. Sifakis. A unified approach for studying the properties of transition systems. TCS, 18, 1982.

    Google Scholar 

  25. J. Sifakis. Property preserving homomorphisms of transition systems. In 4th Workshop on Logics of Programs, Pittsburgh, LNCS 164, Springer Verlag, June 1983.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Patrick Cousot Moreno Falaschi Gilberto Filé Antoine Rauzy

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fernandez, J.C. (1993). Abstract interpretation and verification of reactive systems. In: Cousot, P., Falaschi, M., Filé, G., Rauzy, A. (eds) Static Analysis. WSA 1993. Lecture Notes in Computer Science, vol 724. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57264-3_29

Download citation

  • DOI: https://doi.org/10.1007/3-540-57264-3_29

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57264-0

  • Online ISBN: 978-3-540-48027-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics