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Fields of Logic and Computation pp 227–250Cite as

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

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6300))

Abstract

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.

Most of the material contained in this paper stems, modulo editorial adaptations, from the much longer papers . This paper significantly extends the earlier report .

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Author information

Authors and Affiliations

  1. Institute of Information Systems, Vienna University of Technology, Austria

    Thomas Eiter

  2. Computing Laboratory, Oxford University, United Kingdom

    Georg Gottlob

  3. Fakultät für Informatik, Technische Universität Dortmund, Germany

    Thomas Schwentick

Authors
  1. Thomas Eiter
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  2. Georg Gottlob
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  3. Thomas Schwentick
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Editor information

Editors and Affiliations

  1. Mathematics Department, University of Michigan, 48109-1043, Ann Arbor, MI, USA

    Andreas Blass

  2. School of Computer Science, Tel Aviv University, Ramat Aviv, 69978, Tel Aviv, Israel

    Nachum Dershowitz

  3. Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Wolfgang Reisig

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Eiter, T., Gottlob, G., Schwentick, T. (2010). The Model Checking Problem for Prefix Classes of Second-Order Logic: A Survey. In: Blass, A., Dershowitz, N., Reisig, W. (eds) Fields of Logic and Computation. Lecture Notes in Computer Science, vol 6300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15025-8_13

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  • DOI: https://doi.org/10.1007/978-3-642-15025-8_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15024-1

  • Online ISBN: 978-3-642-15025-8

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