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CTL+ Is Complete for Double Exponential Time

  • Jan Johannsen
  • Martin Lange
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2719)

Abstract

We show that the satisfiability problem for CTL+, the branching time logic that allows boolean combinations of path formulas inside a path quantifier but no nesting of them, is 2-EXPTIME-hard. The construction is inspired by Vardi and Stockmeyer’s 2-EXPTIME-hardness proof of CTL*’s satisfiability problem. As a consequence, there is no subexponential reduction from CTL+ to CTL which preserves satisfiability.

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References

  1. 1.
    M. Adler and N. Immerman. An n! lower bound on formula size. In Proc. 16th Symp. on Logic in Computer Science, LICS’01, pages 197–208, Boston, MA, USA, June 2001. IEEE Computer Society.Google Scholar
  2. 2.
    A. K. Chandra, D. C. Kozen, and L. J. Stockmeyer. Alternation. Journal of the ACM, 28(1):114–133, January 1981.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1–24, 1985.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    E. A. Emerson and J. Y. Halpern. “Sometimes” and “not never” revisited: On branching versus linear time temporal logic. Journal of the ACM, 33(1):151–178, January 1986.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    E. A. Emerson and C. S. Jutla. The complexity of tree automata and logics of programs. SIAM Journal on Computing, 29(1):132–158, February 2000.CrossRefMathSciNetGoogle Scholar
  6. 6.
    E. A. Emerson and C.-L. Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8(3):275–306, 1987.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    O. Kupferman and O. Grumberg. Buy one, get one free!!! Journal of Logic and Computation, 6(4):523–539, August 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    F. Laroussinie, N. Markey, and P. Schnoebelen. Model checking CTL + and FCTL is hard. In Proc. 4th Conf. Foundationsof Software Science and Computation Structures, FOSSACS’01, volume 2030 of LNCS, pages 318–331, Genova, Italy, April 2001. Springer.CrossRefGoogle Scholar
  9. 9.
    M. Y. Vardi and L. Stockmeyer. Improved upper and lower bounds for modal logics of programs. In Proc. 17th Symp. on Theory of Computing, STOC’85, pages 240–251, Baltimore, USA, May 1985. ACM.Google Scholar
  10. 10.
    T. Wilke. CTL+ is exponentially more succinct than CTL. In Proc. 19th Conf. on Foundationsof Software Technology and Theoretical Computer Science, FSTTCS’99, volume 1738 of LNCS, pages 110–121. Springer, 1999.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jan Johannsen
    • 1
  • Martin Lange
    • 1
  1. 1.Institut für InformatikLudwig-Maximilians-Universität MünchenMunichGermany

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