An effective tableau system for the linear time μ-calculus

  • Julian Bradfield
  • Javier Esparza
  • Angelika Mader
Session 2: Fairness, Domination, and the μ-Calculus
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1099)


We present a tableau system for the model checking problem of the linear time μ-calculus. It improves the system of Stirling and Walker by simplifying the success condition for a tableau. In our system success for a leaf is determined by the path leading to it, whereas Stirling and Walker's method requires the examination of a potentially infinite number of paths extending over the whole tableau.


temporal logic linear-time μ-calculus local model-checking tableau systems 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Fit83]
    M. Fitting, Proof Methods for Modal and Intuitionistic Logics (Reidel, 1983).Google Scholar
  2. [HC68]
    G.E. Hughes and M.J. Creswell, An Introduction to Modal Logic, (Methuen and Co., 1968)Google Scholar
  3. [Kai95]
    R. Kaivola, A simple decision method for the linear time mu-calculus, Proc. Int. Workshop on Structures in Concurrency Theory (J. Desel, ed.) (1995)Google Scholar
  4. [Mad92]
    A. Mader, Tableau recycling, Proc. CAV '92, LNCS 663 (1992).Google Scholar
  5. [Mad95]
    A. Mader, Modal μ-calculus, model checking and Gauß elimination, Proc. TACAS'95, to appear in LNCS. (1995)Google Scholar
  6. [Sti87]
    C. P. Stirling, Modal logics for communicating systems. Theoret. Comput. Sci. 49 311–347 (1987).CrossRefGoogle Scholar
  7. [SW90]
    C. Stirling and D. Walker, CCS, liveness, and local model checking in the linear time mu-calculus, Proc. First International Workshop on Automatic Verification Methods for Finite State Systems, LNCS 407 166–178. (1990).Google Scholar
  8. [SW91]
    C. Stirling and D. Walker, Local model checking in the modal mucalculus, Theor. Comput. Sci. 89, 161–177. (1991).CrossRefGoogle Scholar
  9. [Var88]
    M. Vardi, A temporal fixpoint calculus, Proc. 15th PoPL, 250–259. (1988)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Julian Bradfield
    • 1
  • Javier Esparza
    • 2
  • Angelika Mader
    • 2
  1. 1.LFCSUniversity of EdinburghEdinburghUK
  2. 2.Institut für InformatikTechnische Universität MünchenMünchenGermany

Personalised recommendations