Construction of abstract state graphs with PVS

  • Susanne Graf
  • Hassen Saidi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1254)


In this paper, we propose a method for the automatic construction of an abstract state graph of an arbitrary system using the Pvs theorem prover.

Given a parallel composition of sequential processes and a partition of the state space induced by predicates ϕ1, ..., g4 l on the program variables which defines an abstract state space, we construct an abstract state graph, starting in the abstract initial state. The possible successors of a state are computed using the Pvs theorem prover by verifying for each index i if ϕi or ¬ϕi is a postcondition of it. This allows an abstract state space exploration for arbitrary programs.


abstract interpretation state graph exploration theorem proving 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BBC+96]
    N. Bjorner, A. Browne, E. Chang, M. Colon, A. Kapur, Z. Manna, H. Sipma, and T. Uribe. Step: Deductive-algorithmic verification of reactive and realtime systems. In CAV'96. LNCS 1102, 1996.Google Scholar
  2. [BBL97]
    K. Baukus, S. Bensalem, and Y. Lakhnech. A PVS based tool for the verification of invariants. submitted to CAV'97.Google Scholar
  3. [BLS96]
    S. Bensalem, Y. Lakhnech, and H. Saidi, Powerful techniques for the automatic generation of invariants. In CAV'96, LNCS 1102, 1996.Google Scholar
  4. [CC77]
    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
  5. [CGL94]
    E.M. Clarke, O. Grumberg, and D.E. Long. Model checking and abstraction. ACM Transactions on Programming Languages and Systems, 16(5), 1994.Google Scholar
  6. [CM88]
    K. M. Chandy and J. Misra. Parallel Program Design. 1988.Google Scholar
  7. [Dam96]
    D. Dams. Abstract interpretation and partition refinement for model checking. Phd Thesis, Technical University of Eindhoven, July 1996.Google Scholar
  8. [DF95]
    J. Dingel and Th. Filkorn. Model checking for infinite state systems using data abstraction, assumption-commitment style reasoning and theorem proving. In CAV'95. LNCS 939, 1995.Google Scholar
  9. [DGG93]
    D. Dams, O. Grumberg, and R. Gerth. Generation of reduced models for checking fragments of CTL. In CAV'93, LNCS 697, 1993.Google Scholar
  10. [DOTY96]
    C. Daws, A. Olivero, S. Tripakis, and S. Yovine. The tool KRONOS. In Hybrid Systems III, Verification and Control, LNCS 1066, 1996.Google Scholar
  11. [FGK+96]
    J.-C. Fernandez, H. Garavel, A. Kerbrat, R. Mateescu, L. Mounier and M. Sighireanu. CADP (Caesar/Aldébaran Development Package): A protocol validation and verification toolbox. In CAV'96. LNCS 1102.Google Scholar
  12. [GL93]
    S. Graf and C. Loiseaux. A tool for symbolic program verification and abstraction. In CAV'93. LNCS 697, 1993.Google Scholar
  13. [Gra95]
    S. Graf. Characterization of a sequentially consistent memory and verification of a cache memory by abstraction. accepted to Distributed Computing.Google Scholar
  14. [GS96]
    S. Graf and H. Saidi. Verifying invariants using theorem proving. In CAV'96, LNCS 1102, 1996.Google Scholar
  15. [GvdP93]
    J.F Groote and J. van de Pol. A bounded retransmission protocol for large data packets. Technical Report Logic Group 100, Utrecht University, 1993.Google Scholar
  16. [HGD95]
    H. Hungar, O. Grumberg, and W. Damm. What if model checking must be truly symbolic. In TACAS'95. LNCS 1019, 1995.Google Scholar
  17. [HH95]
    T. Henzinger and P.H. Ho. Hytech: the Cornell hybrid technology tool. In Hybrid Systems II. LNCS 999, 1995.Google Scholar
  18. [HPR94]
    N. Halbwachs, Y.-E. Proy, and P. Raymond. Verification of linear hybrid systems by means of convex approximations. In SAS'94. LNCS 864.Google Scholar
  19. [HS96]
    K. Havelund and N. Shankar. Experiments in theorem proving and model checking for protocol verification. In Formal Methods in Europe'96, 1996.Google Scholar
  20. [HSV94]
    L. Helmink, M. Sellink, and F. Vaandrager. Proof-checking a data link protocol. Technical report CS-R9420, CWI, 1994.Google Scholar
  21. [KDG95]
    P. Kelb, D. Dams, and R. Gerth. Efficient symbolic model-checking for the full μ-calculus using compositional abstractions. Tech Rep 31, TU Eindhoven, 1995.Google Scholar
  22. [Kur94]
    R.P. Kurshan. Computer-Aided Verification of Coordinating processes, the automata theoretic approach. Princeton Series in Computer Science. 1994.Google Scholar
  23. [LGS+95]
    C. Loiseaux, S. Graf, J. Sifakis, A. Bouajjani, and S. Bensalem. Property preserving abstractions for the verification of concurrent systems. Formal Methods in System Design, Vol 6, Iss 1, 1995 Google Scholar
  24. [Sa97]
    H. Saïdi. The invariant checker: Automated deductive verification of reactive systems. In this volume.Google Scholar
  25. [Sif82]
    Joseph Sifakis. A unified approach for studying the properties of transition systems. TCS 18, 1982.Google Scholar
  26. [SOR93]
    N. Shankar, S. Owre, and J.M. Rushby. A Tutorial on Specification and Verification using PVS. SRI International, Menlo Park, CA, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Susanne Graf
    • 1
  • Hassen Saidi
    • 1
  1. 1.Centre EquationVERIMAGGrenoble-Gières

Personalised recommendations