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The Complexity of Positive First-Order Logic without Equality II: The Four-Element Case

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Computer Science Logic (CSL 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6247))

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Abstract

We study the complexity of evaluating positive equality-free sentences of first-order logic over fixed, finite structures \(\mathcal{B}\). This may be seen as a natural generalisation of the non-uniform quantified constraint satisfaction problem QCSP \((\mathcal{B})\). Extending the algebraic methods of a previous paper, we derive a complete complexity classification for these problems as \(\mathcal{B}\) ranges over structures of domain size 4. Specifically, each problem is either in L, is NP-complete, is co-NP-complete or is Pspace-complete.

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Author information

Authors and Affiliations

  1. School of Engineering and Computing Sciences, Durham University, Science Site, South Road, Durham, DH1 3LE, U.K.

    Barnaby Martin

  2. The MathWorks, Matrix House, Cambridge, CB4 0HH, U.K.

    Jos Martin

Authors
  1. Barnaby Martin
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  2. Jos Martin
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Editor information

Editors and Affiliations

  1. Computer Laboratory, University of Cambridge, J.J. Thomson Avenue, CB3 0FD, Cambridge, UK

    Anuj Dawar

  2. Formal Methods in Systems Engineering, Vienna University of Technology, Favoritenstr. 9-11, 1040, Vienna, Austria

    Helmut Veith

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Martin, B., Martin, J. (2010). The Complexity of Positive First-Order Logic without Equality II: The Four-Element Case. In: Dawar, A., Veith, H. (eds) Computer Science Logic. CSL 2010. Lecture Notes in Computer Science, vol 6247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15205-4_33

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  • DOI: https://doi.org/10.1007/978-3-642-15205-4_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15204-7

  • Online ISBN: 978-3-642-15205-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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