The Model Checking Problem for Prefix Classes of Second-Order Logic: A Survey

  • Thomas Eiter
  • Georg Gottlob
  • Thomas Schwentick
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6300)


In this paper, we survey results related to the model checking problem for second-order logic over classes of finite structures, including word structures (strings), graphs, and trees, with a focus on prefix classes, that is, where all quantifiers (both first- and second-order ones) are at the beginning of formulas. A complete picture of the prefix classes defining regular and non-regular languages over strings is known, which nearly completely coincides with the tractability frontier; some complexity issues remain to be settled, though. Over graphs and arbitrary relational structures, the tractability frontier is completely delineated for the existential second-order fragment, while it is less explored for trees. Besides surveying some of the results, we mention some open issues for research.


Finite Model Theory Gurevich’s Classifiability Theorem Model Checking Monadic Second-Order Logic Regular Languages Second-Order Logic 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Thomas Eiter
    • 1
  • Georg Gottlob
    • 2
  • Thomas Schwentick
    • 3
  1. 1.Institute of Information SystemsVienna University of TechnologyAustria
  2. 2.Computing LaboratoryOxford UniversityUnited Kingdom
  3. 3.Fakultät für InformatikTechnische Universität DortmundGermany

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