Journal of Computer Science and Technology

, Volume 17, Issue 6, pp 665–671 | Cite as

A graphical μ-calculus and local model checking

Regular Papers
  • 25 Downloads

Abstract

A graphical notation for the propositional μ-calculus, calledmodal graphs, is presented. It is shown that both the textual and equational presentations of the μ-calculus can be translated into modal graphs. A model checking algorithm based on such graphs is proposed. The algorithm istruly local in the sense that it only generates the parts of the underlying search space which are necessary for the computation of the final result. The correctness of the algorithm is proven and its complexity analysed.

Keywords

model checking μ-calculus modal graphs local algorithms 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Clarke E M, Grumberg O, Peled D A. Model Checking. The MIT Press, 1999.Google Scholar
  2. [2]
    Bradfield J, Stirling C. Modal logics and mu-calculus: An introduction. InHandbook of Process Algebra, Ponse A, Bergstra J A, Smolka S A (eds.), Elsevier, 2001, pp.293–330.Google Scholar
  3. [3]
    Emerson E A, Lei C-L. Efficient model checking in fragments of the propositional mu-calculus. InProc. Logic in Computer Science, Cambridge, Massachusetts, IEEE Press, 1986, pp.267–278.Google Scholar
  4. [4]
    Cleaveland R. Tableau-based model checking in the propositional mu-calculus.Acta Informatica, 1990, 27(4): 724–747.MathSciNetGoogle Scholar
  5. [5]
    Andersen H R. Model checking and boolean graphs.Theoretical Computer Science, 1994, 126: 3–30.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Stirling C, Walker D. Local model checking in the modal mu-calculus.Theoretical Computer Science, 1991, 89: 161–177.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Larsen K G. Efficient local correctness checking. InProc. Computer Aided Verification, Montreal, pp.30–43, Lecture Notes in Computer Science 663, 1992, Springer-Verlag.Google Scholar
  8. [8]
    Liu X, Ramakrishnan C R, Scott A Smolka. Fully local and efficient evaluation of alternating fixed points. InProc. Tools and Algorithms for the Construction of Systems, Lisbon, pp.5–19, Lecture Notes in Computer Science 1384, Springer-Verlag, 1998.Google Scholar
  9. [9]
    Tarski A. A lattice-theoretical fixpoint theorem and its applications.Pacific Journal of Mathematics, 1955, 5: 285–309.MATHMathSciNetGoogle Scholar

Copyright information

© Science Press, Beijing China and Allerton Press Inc. 2002

Authors and Affiliations

  1. 1.Laboratory for Computer Science, Institute of SoftwareThe Chinese Academy of SciencesBeijingP.R. China

Personalised recommendations