Advertisement

The Expressive Power of Two-Variable Least Fixed-Point Logics

  • Martin Grohe
  • Stephan Kreutzer
  • Nicole Schweikardt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3618)

Abstract

The present paper gives a classification of the expressive power of two-variable least fixed-point logics. The main results are:

  1. 1

    The two-variable fragment of monadic least fixed-point logic with parameters is as expressive as full monadic least fixed-point logic (on binary structures).

     
  2. 2

    The two-variable fragment of monadic least fixed-point logic without parameters is as expressive as the two-variable fragment of binary least fixed-point logic without parameters.

     
  3. 3

    The two-variable fragment of binary least fixed-point logic with parameters is strictly more expressive than the two-variable fragment of monadic least fixed-point logic with parameters (even on finite strings).

     

Keywords

Modal Logic Monotone Operator Expressive Power Binary Signature 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arnold, A., Niwiński, D.: Rudiments of μ-calculus. North Holland, Amsterdam (2001)Google Scholar
  2. 2.
    Cosmadakis, S.S.: The complexity of evaluating relational queries. Information and Control 58, 101–112 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Dawar, A.: Feasible computation through model theory. PhD thesis, Univ. of Pennsylvania (1993)Google Scholar
  4. 4.
    Dawar, A., Lindell, S., Weinstein, S.: Infinitary logic and inductive definability over finite structures. Information and Computation 119, 160–175 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Dawar, A., Grädel, E., Kreutzer, S.: Inflationary fixed points in modal logic. ACM Transactions on Computational Logic 5, 282–315 (2004)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Dziembowski, S.: Bounded-variable fixpoint queries are pspace-complete. In: van Dalen, D., Bezem, M. (eds.) CSL 1996. LNCS, vol. 1258, pp. 89–105. Springer, Heidelberg (1997)Google Scholar
  7. 7.
    Ebbinghaus, H.-D., Flum, J.: Finite model theory, 2nd edn. Springer, New York (1999)zbMATHGoogle Scholar
  8. 8.
    Grädel, E., Otto, M.: On Logics with Two Variables. Theoretical Computer Science 224, 73–113 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Grädel, E., Otto, M., Rosen, E.: Undecidability Results for Two-Variable Logics. Archive for Mathematical Logic 38, 313–354 (1999) (Journal version of STACS 1997 paper)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Grohe, M.: Finite variable logics in descriptive complexity theory. Bulletin of Symbolic Logic 4, 345–398 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Grohe, M., Schweikardt, N.: Comparing the succinctness of monadic query languages over finite trees. RAIRO - Theoretical Informatics and Applications (ITA) 38, 343–373 (2004); Journal version of CSL 2003 paperzbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Hodkinson, I.: Finite variable logics. Bull. Europ. Assoc. Theor. Comp. Sci. 51, 111–140 (1993)zbMATHGoogle Scholar
  13. 13.
    Immerman, N.: Relational queries computable in polynomial time. Information and Control 68, 86–104 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Kolaitis, P., Vardi, M.: On the expressive power of variable-confined logics. In: Proc. of LICS 1996, pp. 348–359 (1996)Google Scholar
  15. 15.
    Libkin, L.: Elements of Finite Model Theory. Springer, Heidelberg (2004)zbMATHGoogle Scholar
  16. 16.
    Otto, M.: Bounded variable logics and counting – A study in finite models. Lecture Notes in Logic, vol. 9, p. IX+183. Springer, Heidelberg (1997)zbMATHGoogle Scholar
  17. 17.
    Schweikardt, N.: On the expressive power of monadic least fixed point logic. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 1123–1135. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  18. 18.
    Vardi, M.Y.: On the complexity of bounded-variable queries. In: PODS 1995: 14th ACM Symposium on Principles of Database Systems, pp. 266–276 (1995)Google Scholar
  19. 19.
    Vardi, M.Y.: The complexity of relational query languages. In: STOC 1982: 14th Annual ACM Symposium on the Theory of Computing, pp. 137–146 (1982)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Martin Grohe
    • 1
  • Stephan Kreutzer
    • 1
  • Nicole Schweikardt
    • 1
  1. 1.Institut für InformatikHumboldt-UniversitätBerlin

Personalised recommendations