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Complexity of First-Order Logic

  • Chapter
Elements of Finite Model Theory

Part of the book series: Texts in Theoretical Computer Science ((TTCS))

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Abstract

The goal of this chapter is to study the complexity of queries expressible in FO. We start with the general definition of different ways of measuring the complexity of a logic over finite structures: these are data, expression, and combined complexity. We then connect FO with Boolean circuits and establish some bounds on the data complexity. We also consider the issue of uniformity for a circuit model, and study it via logical definability. We then move to the combined complexity of FO, and show that it is much higher than the data complexity. Finally, we investigate an important subclass of FO queries — conjunctive queries — which play a central role in database theory.

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Authors and Affiliations

  1. Department of Computer Science, University of Toronto, M5S 3H5, Toronto, ON, Canada

    Prof. Leonid Libkin

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  1. Prof. Leonid Libkin
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© 2004 Springer-Verlag Berlin Heidelberg

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Libkin, L. (2004). Complexity of First-Order Logic. In: Elements of Finite Model Theory. Texts in Theoretical Computer Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07003-1_6

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  • DOI: https://doi.org/10.1007/978-3-662-07003-1_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05948-3

  • Online ISBN: 978-3-662-07003-1

  • eBook Packages: Springer Book Archive

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