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URN: urn:nbn:de:0030-drops-23670
URL: http://drops.dagstuhl.de/opus/volltexte/2010/2367/

Martin, Barnaby ; Martin, Jos

The complexity of positive first-order logic without equality II: The four-element case

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Abstract

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

BibTeX - Entry

@InProceedings{martin_et_al:DSP:2010:2367,
  author =	{Barnaby Martin and Jos Martin},
  title =	{The complexity of positive first-order logic without equality II: The four-element case},
  booktitle =	{The Constraint Satisfaction Problem: Complexity and Approximability},
  year =	{2010},
  editor =	{Andrei A. Bulatov and Martin Grohe and Phokion G. Kolaitis and Andrei Krokhin},
  number =	{09441},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2367},
  annote =	{Keywords: Quantified constraints, Galois connection}
}

Keywords: Quantified constraints, Galois connection
Seminar: 09441 - The Constraint Satisfaction Problem: Complexity and Approximability
Issue date: 2010
Date of publication: 07.01.2010


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