On model-checking for fragments of μ-calculus

  • E. A. Emerson
  • C. S. Jutla
  • A. P. Sistla
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 697)


In this paper we considered two different fragments of μ-calculus, logics L1 and L2. We gave model checking algorithms for logics L1 and L2 which are of complexity O(m2n) where m is the length of the formula and n is the size of the structure. We have shown that the logic L2 is as expressive as ECTL* given in [13]. In additions to these results, we have shown that the model checking problem for the μ-calculus is equivalent to the non-emptiness problem of parity tree automata.

It will be interesting to investigate if there is a model checking algorithm for the logics L1 and L2 which is only of complexity O(mn) instead of O(m2n. Of course, determining if the model checking problem for the full μ-calculus is in P or not, is also an open problem.


Model Check Atomic Proposition Kripke Structure Tree Automaton Model Check Problem 
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.
    R. Cleaveland, Tableux-based model checking in the propositional μ-calculus, Acta Informatica, 27:725–747, 1990.Google Scholar
  2. 2.
    R. Cleaveland and B. Steffen, A linear-time model-checking for alternation free modal fi-calculus, Proceedings of the 3rd workshop on Computer Aided Verification, Aalborg, LNCS, Springer-Verlag, July 1991.Google Scholar
  3. 3.
    R. Cleaveland and B. Steffen, Faster model-checking for modal μ-calculus, Proceedings of the 4th workshop on Computer Aided Verification, Montreal, July 1991.Google Scholar
  4. 4.
    E. A. Emerson, E. M. Clarke, Characterizing correctness properties of parallel programs Using Fixpoints, Proceedings of the International Conference on Automata, Languages and Programming, 1980.Google Scholar
  5. 5.
    E.A. Emerson and C. S. Jutla, Tree Automata, Mu-calculus and Determinacy, Proceedings of the 1991 IEEE Symposium on Foundations of Computer Science.Google Scholar
  6. 6.
    E. A, Emerson and C. Leis, Efficient model-checking in fragments of μ-calculus, Proceedings of Symposium on Logic in Computer Science, 1986.Google Scholar
  7. 7.
    E. A. Emerson and C. Leis, Modalities for Model Checking, Science of Computer Programming, 1987.Google Scholar
  8. 8.
    D. Kozen, Results on the propositional μ-calculus, Theoretical Computer Science, 27, 1983.Google Scholar
  9. 9.
    A.W. Mostowski, Regular Expressions for Infinite trees and a standard form of automata, in: A. Skowron, ed., Computation Theory, LNCS, vol 208, 1984, Springer-Verlag.Google Scholar
  10. 10.
    D. Niwinski, Fixed-points Vs. Infinite Generation, Proceedings of the Third IEEE Symposium on Logic in Computer Science, 1988.Google Scholar
  11. 11.
    C. Stirling, D. Walker, Local model-checking in modal μ-calculus, Proceedings of TAPSOFT, 1989.Google Scholar
  12. 12.
    R. S. Streett and E. A. Emerson, An automata theoretic decision procedure for Propositional μ-calculus, Proceedings of the International Conference on Automata, Languages and Programming, 1984.Google Scholar
  13. 13.
    M. Vardi and P. Wolper, Yet Another Process Logic, Proceedings of the workshop on Logics of Programs, Pittsburgh, 1983, also appeared in Lecture Notes in Computer Science.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • E. A. Emerson
    • 1
  • C. S. Jutla
    • 2
  • A. P. Sistla
    • 3
  1. 1.Department of Computer ScienceUniversity of Texas at AustinAustin
  2. 2.I.B.M. Thomas J. Watson Research LaboratoriesUSA
  3. 3.Department of Electrical Engineering and Computer ScienceUniversity of Illinois at ChicagoChicago

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