A tool set for deciding behavioral equivalences

  • Jean-Claude Fernandez
  • Laurent Mounier
Invited Lectures
Part of the Lecture Notes in Computer Science book series (LNCS, volume 527)


This paper deals with verification methods based on equivalence relations between labeled transition systems. More precisely, we are concerned by two practical needs: how to efficiently minimize and compare labeled transition systems with respect to bisimulation or simulation-based equivalence relations.

First, we recall the principle of the classical algorithms for the existing equivalence relations, which are based on successive partition refinements of the state space of the labeled transition systems under consideration. However, in spite of their theoretical efficiency, the main drawback of these algorithms is that they require to generate and to store in memory the whole labeled transition systems to be compared or minimized. Therefore, the size of the systems which can be handled in practice remains limited. We propose here another approach, allowing to combine the generation and the verification phases, which is based on two algorithms respectively devoted to the comparison (“on the fly” comparison) and the minimization (minimal model generation) of labeled transition systems. Then, we present the results obtained when implementing some of these algorithms within the tool Aldébaran.


Equivalence Relation Label Transition System Execution Sequence Verification Method Initial Partition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BFG*91]
    A. Bouajjani, J.C. Fernandez, S. Graf, C. Rodriguez, and J. Sifakis. Safety for branching time semantics. In 18th ICALP, july 1991.Google Scholar
  2. [BFH90a]
    A. Bouajjani, J. C. Fernandez, and N. Halbwachs. On the verification of safety properties. Tech. report, Spectre L 12, IMAG, Grenoble, march 1990.Google Scholar
  3. [BFH90b]
    A. Bouajjani, J.C. Fernandez, and N. Halbwachs. Minimal model generation. In Workshop on Computer-aided Verification, to appear in LNCS, Springer Verlag, june 1990.Google Scholar
  4. [BHR84]
    S. D. Brookes, C.A.R Hoare, and A.W. Roscoe. Theory of communicating sequential processes. JACM, 31(3), 1984.Google Scholar
  5. [CES86]
    E. M. Clarke, E. A. Emerson, and A. P. Sistla. Automatic verification of finitestate concurrent systems using temporal logic spec ifications. TOPLAS, 8(2), 1986.Google Scholar
  6. [Cle90]
    R. Cleaveland. On automatically distinguishing inequivalent processes. In Workshop on Computer-Aided Verification, june 1990.Google Scholar
  7. [CPS90]
    R. Cleaveland, J. Parrow, and B. Steffen. The concurrency workbench. In Workshop on Computer-Aided Verification, june 1990.Google Scholar
  8. [CVWY90]
    C. Courcoubetis, M. Vardi, P. Wolper, and M. Yannakakis. Memory efficient algorithms for the verification of temporal properties. In Workshop on Computer-Aided Verification, june 1990.Google Scholar
  9. [dSV89]
    R. de Simone and D. Vergamini. Aboard Auto. Rapport Technique 111, INRIA, Sophia Antipolis, 1989.Google Scholar
  10. [Fer90]
    J. C. Fernandez. An implementation of an efficient algorithm for bisimulation equivalence. Science of Computer Programming, 13(2–3), May 1990.Google Scholar
  11. [FM91]
    J.-C. Fernandez and L. Mounier. “on the fly” verification of behavioural equivalences and preorders. In Workshop on Computer-aided Verification, To appear, july 1–4 1991.Google Scholar
  12. [Gla90]
    R.J. van Glabbeek. The Linear Time-Branching Time Spectrum. Technical Report CS-R9029, Centre for Mathematics and Computer Science, 1990.Google Scholar
  13. [GS90]
    Hubert Garavel and Joseph Sifakis. Compilation and verification of lotos specifications. In L. Logrippo, R. L. Probert, and H. Ural, editors, Proceedings of the 10th International Symposium on Protocol Specification, Testing and Verification (Ottawa), IFIP, North-Holland, Amsterdam, June 1990.Google Scholar
  14. [GV90]
    Jan Friso Groote and Frits Vaandrager. An Efficient Algorithm for Branching Bisimulation and Stuttering Equivalence. CS-R 9001, Centrum voor Wiskunde en Informatica, Amsterdam, January 1990.Google Scholar
  15. [GW89]
    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
  16. [JJ89]
    Claude Jard and Thierry Jeron. On-line model-checking for finite linear temporal logic specifications. In International Workshop on Automatic Verification Methods for Finite State Systems, LNCS 407, Springer Verlag, 1989.Google Scholar
  17. [JJ91]
    Claude Jard and Thierry Jéron. Bounded-memory algorithms for verification on-the-fly. In K. G. Larsen, editor, Proceedings of the 3rd Workshop on Computer-Aided Verification (Aalborg, Denmark), July 1991. to appear.Google Scholar
  18. [KS83]
    P. Kanellakis and S. Smolka. Ccs expressions, finite state processes and three problems of equivalence. In Proceedings ACM Symp. on Principles of Distribued Computing, 1983.Google Scholar
  19. [Mil80]
    R. Milner. A calculus of communication systems. In LNCS 92, Springer Verlag, 1980.Google Scholar
  20. [NMV90]
    R. De Nicola, U. Montanari, and F.W. Vaandrager. Back and Forth Bisimulations. CS-R 9021, Centrum voor Wiskunde en Informatica, Amsterdam, 1990.Google Scholar
  21. [NV90]
    R. De Nicola and F. Vaandrager. Three logics for branching bisimulation. In Proc. of Fifth Symp. on Logic in Computer Science, Computer Society Press, 1990.Google Scholar
  22. [Par81]
    D. Park. Concurrency and automata on infinite sequences. In 5th GI-Conference on Theorical Computer Science, Springer Verlag, 1981. LNCS 104.Google Scholar
  23. [PT87]
    R. Paige and R. Tarjan. Three partition refinement algorithms. SIAM J. Comput., No. 6, 16, 1987.Google Scholar
  24. [QPF88]
    Juan Quemada, Santiago Pavón, and Angel Fernández. Transforming lotos specifications with lola: the parametrized expansion. In Kenneth J. Turner, editor, Proceedings of the 1st International Conference on Formal Description Techniques FORTE'88 (Stirling, Scotland), pages 45–54, North-Holland, Amsterdam, September 1988.Google Scholar
  25. [Ras91]
    A. Rasse. Error diagnosis in finite communicating systems. In Workshop on Computer-aided Verification, To appear, july 1–4 1991.Google Scholar
  26. [RRSV87]
    J.L. Richier, C. Rodriguez, J. Sifakis, and J. Voiron. Xesar: A Tool for Protocol Validation. User's Guide. LGI-Imag, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Jean-Claude Fernandez
    • 1
  • Laurent Mounier
    • 1
  1. 1.LGI-IMAG, IMAG CampusGrenoble cedexFrance

Personalised recommendations