Automata for the modal μ-calculus and related results

  • David Janin
  • Igor Walukiewicz
Contributed Papers Formal Calculi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 969)


The propositional Μ-calculus as introduced by Kozen in [4] is considered. The notion of disjunctive formula is defined and it is shown that every formula is semantically equivalent to a disjunctive formula. For these formulas many difficulties encountered in the general case may be avoided. For instance, satisfiability checking is linear for disjunctive formulas. This kind of formula gives rise to a new notion of finite automaton which characterizes the expressive power of the Μ-calculus over all transition systems.


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  1. 1.
    O. Bernholtz and O. Grumberg. Branching time temporal logic and amorphous tree automata. In Proc. 4th Conference on Concurrency Theory, volume 715 of Lecture Notes in Computer Science, pages 262–277. Springer-Verlag, 1993.Google Scholar
  2. 2.
    E.A. Emerson and C.S. Jutla. The complexity of tree automata and logics of programs. In 29th IEEE Symp. on Foundations of Computer Science, 1988.Google Scholar
  3. 3.
    E.A. Emerson and C.S. Jutla. Tree automata, mu calculus and determinacy. In Proc. FOCS 91, 1991.Google Scholar
  4. 4.
    D. Kozen. Results on the propositional mu-calculus. Theoretical Computer Science, 27:333–354, 1983.CrossRefGoogle Scholar
  5. 5.
    D. Kozen. A finite model theorem for the propositional Μ-calculus. Studa Logica, 47(3):234–241, 1988.Google Scholar
  6. 6.
    A.W. Mostowski. Regular expressions for infinite trees and a standard form of automta. In A. Skowron, editor, Fith Symposium on Computation Theory, volume 208 of LNCS, pages 157–168, 1984.Google Scholar
  7. 7.
    D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267–276, 1987.CrossRefGoogle Scholar
  8. 8.
    D. Niwiński. Fixed points vs. infinite generation. In Proc. 3rd. IEEE LICS, pages 402–409, 1988.Google Scholar
  9. 9.
    R.S. Street and E.A. Emerson. An automata theoretic procedure for the propositional mu-calculus. Information and Computation, 81:249–264, 1989.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • David Janin
    • 1
  • Igor Walukiewicz
    • 2
  1. 1.Laboratoire Bordelais de Recherche en Informatique U.E.R. de Mathématiques et d'InformatiqueUniversité de Bordeaux ITalence CedexFrance
  2. 2.Basic Research in Computer Science Department of Computer ScienceUniversity of AarhusAarhus CDenmark

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