A Generic On-the-Fly Solver for Alternation-Free Boolean Equation Systems

  • Radu Mateescu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2619)


Boolean Equation Systems (Bess) offer a useful representation for various verification problems on finite-state concurrent systems, such as equivalence/preorder checking and model checking. In particular, on-the-fly resolution methods enable a demand-driven construction of the Bes (and hence, of the state space) during verification. In this paper, we present a generic library dedicated to on-the-fly resolution of alternation-free Bess. Four resolution algorithms are currently provided by the library: A1, A2 are general, the latter being optimized to produce small-depth diagnostics, and A3, A4 are specialized for handling acyclic and disjunctive/conjunctive Bess in a memory-efficient way. The library is developed within the Cadp toolbox and serves as engine for on-the-fly equivalence/preorder checking modulo five widely-used relations, and for model checking of alternation-free μ-calculus.


Model Check Temporal Logic Propositional Variable Label Transition System Resolution Algorithm 
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.


  1. 1.
    H. R. Andersen. Model checking and boolean graphs. TCS, 126(1):3–30, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    J. C. M. Baeten and R. J. van Glabbeek. Another Look at Abstraction in Process Algebra. In ICALP’87, Lncs 267, pp. 84–94.Google Scholar
  3. 3.
    A. Bouajjani, J-C. Fernandez, S. Graf, C. Rodríguez, and J. Sifakis. Safety for Branching Time Semantics. In ICALP’91, Lncs 510.Google Scholar
  4. 4.
    E. M. Clarke, E. A. Emerson, and A. P. Sistla. Automatic Verification of Finite-State Concurrent Systems using Temporal Logic Specifications. ACM Trans. on Prog. Lang. and Systems, 8(2):244–263, April 1986.zbMATHCrossRefGoogle Scholar
  5. 5.
    R. Cleaveland and B. Steffen. Computing behavioural relations, logically. In ICALP’91, Lncs 510, pp. 127–138.Google Scholar
  6. 6.
    R. Cleaveland and B. Steffen. A Linear-Time Model-Checking Algorithm for the Alternation-Free Modal Mu-Calculus. In CAV’91, Lncs 575, pp. 48–58.Google Scholar
  7. 7.
    X. Du, S. A. Smolka, and R. Cleaveland. Local Model Checking and Protocol Analysis. Springer STTT Journal, 2(3):219–241, 1999.zbMATHGoogle Scholar
  8. 8.
    E. A. Emerson and C-L. Lei. Efficient Model Checking in Fragments of the Propositional Mu-Calculus. In LICS’86, pp. 267–278.Google Scholar
  9. 9.
    A. Fantechi, S. Gnesi, and G. Ristori. From ACTL to Mu-Calculus. In ERCIM’92 Ws. on Theory and Practice in Verification (Pisa, Italy), IEI-CNR, pp. 3–10, 1992.Google Scholar
  10. 10.
    J-C. Fernandez, H. Garavel, A. Kerbrat, R. Mateescu, L. Mounier, and M. Sighireanu. CADP (CÆSAR/ALDEBARAN Development Package): A Protocol Validation and Verification Toolbox. In CAV’96, Lncs 1102, pp. 437–440.Google Scholar
  11. 11.
    J-C. Fernandez, C. Jard, Th. Jéron, L. Nedelka, and C. Viho. Using On-the-Fly Verification Techniques for the Generation of Test Suites. In CAV’96, Lncs 1102.Google Scholar
  12. 12.
    J-C. Fernandez and L. Mounier. “On the Fly” Verification of Behavioural Equivalences and Preorders. In CAV’91, Lncs 575.Google Scholar
  13. 13.
    M. J. Fischer and R. E. Ladner. Propositional Dynamic Logic of Regular Programs. J. of Comp. and System Sciences, (18):194–211, 1979.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    H. Garavel. OPEN/CÆSAR: An Open Software Architecture for Verification, Simulation, and Testing. In TACAS’98, Lncs 1384, pp. 68–84.Google Scholar
  15. 15.
    A. Mader. Verification of Modal Properties Using Boolean Equation Systems. VERSAL 8, Bertz Verlag, Berlin, 1997.Google Scholar
  16. 16.
    R. Mateescu. Efficient Diagnostic Generation for Boolean Equation Systems. In TACAS’00, Lncs 1785, pp. 251–265.Google Scholar
  17. 17.
    R. Mateescu. Local Model-Checking of Modal Mu-Calculus on Acyclic Labeled Transition Systems. In TACAS’02, Lncs 2280, pp. 281–295.Google Scholar
  18. 18.
    R. Mateescu and M. Sighireanu. Efficient On-the-Fly Model-Checking for Regular Alternation-Free Mu-Calculus. Science of Comp. Programming, 2002. To appear.Google Scholar
  19. 19.
    R. Milner. Communication and Concurrency. Prentice-Hall, 1989.Google Scholar
  20. 20.
    R. De Nicola and F. W. Vaandrager. Action versus State based Logics for Transition Systems. In Semantics of Concurrency, Lncs 469, pp. 407–419.Google Scholar
  21. 21.
    R. De Nicola, U. Montanari, and F. Vaandrager. Back and Forth Bisimulations. CS R9021, CWI, Amsterdam, May 1990.Google Scholar
  22. 22.
    D. Park. Concurrency and Automata on Infinite Sequences. In Th. Comp. Sci., Lncs 104, pp. 167–183.CrossRefGoogle Scholar
  23. 23.
    R. J. van Glabbeek and W. P. Weijland. Branching-Time and Abstraction in Bisimulation Semantics. In Proc. IFIP 11th World Computer Congress, 1989.Google Scholar
  24. 24.
    B. Yang, R.E. Bryant, D. R. O’Hallaron, A. Biere, O. Condert, G. Janssen, R.K. Ranjan, and F. Somenzi. A Performance Study of BDD-Based Model-Checking. In FMCAD’98, Lncs 1522, pp. 255–289.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Radu Mateescu
    • 1
  1. 1.Inria Rhône-Alpes / VasyMontbonnot Saint MartinFrance

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