Advertisement

The Complexity of Independence-Friendly Fixpoint Logic

  • Julian Bradfield
  • Stephan Kreutzer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3634)

Abstract

We study the complexity of model-checking for the fixpoint extension of Hintikka and Sandu’s independence-friendly logic. We show that this logic captures ExpTime; and by embedding PFP, we show that its combined complexity is ExpSpace-hard, and moreover the logic includes second order logic (on finite structures).

Keywords

Modal Logic Free Variable Choice Function Winning Strategy Skolem Function 
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. [AV89]
    Abiteboul, S., Vianu, V.: Fixpoint extensions of first-order logic and Datalog-like languages. In: Proc. 4th IEEE Symp. on Logic in Computer Science (LICS), pp. 71–79 (1989)Google Scholar
  2. [Bra99]
    Bradfield, J.C.: Fixpoints in arithmetic, transition systems and trees. Theoretical Informatics and Applications 33, 341–356 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  3. [Bra00]
    Bradfield, J.C.: Independence: logics and concurrency. In: Clote, P.G., Schwichtenberg, H. (eds.) CSL 2000. LNCS, vol. 1862, pp. 247–261. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  4. [Bra03]
    Bradfield, J.C.: Parity of imperfection. In: Baaz, M., Makowsky, J.A. (eds.) CSL 2003. LNCS, vol. 2803, pp. 72–85. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. [BrF02]
    Bradfield, J.C., Fröschle, S.B.: Independence-friendly modal logic and true concurrency. Nordic J. Computing 9, 102–117 (2002)zbMATHGoogle Scholar
  6. [EF99]
    Ebbinghaus, H.-D., Flum, J.: Finite Model Theory, 2nd edn. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  7. [End70]
    Enderton, H.B.: Finite partially ordered quantifiers. Z. für Math. Logik u. Grundl. Math. 16, 393–397 (1970)zbMATHCrossRefMathSciNetGoogle Scholar
  8. [Gra03]
    Grädel, E.: Finite Model Theory and Descriptive Complexity. In: Finite Model Theory and Its Applications, Springer, Heidelberg (2005), See http://wwwmgi.informatik.rwth-aachen.de/Publications/pub/graedel/Gr-FMTbook.ps Google Scholar
  9. [HiS96]
    Hintikka, J., Sandu, G.: A revolution in logic? Nordic J. Philos. Logic 1(2), 169–183 (1996)zbMATHMathSciNetGoogle Scholar
  10. [Hod97]
    Hodges, W.: Compositional semantics for a language of imperfect information. Int. J. IGPL 5(4), 539–563Google Scholar
  11. [Pie00]
    Pietarinen, A.: Games logic plays. Informational independence in gametheoretic semantics. D.Phil. thesis, Univ Sussex (2000)Google Scholar
  12. [Wal70]
    Walkoe Jr., W.J.: Finite partially-ordered quantification. J. Symbolic Logic 35, 535–555 (1970)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Julian Bradfield
    • 1
  • Stephan Kreutzer
    • 2
  1. 1.Laboratory for Foundations of Computer ScienceUniversity of Edinburgh 
  2. 2.Institut für InformatikHumboldt UniversitätBerlinGermany

Personalised recommendations