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

Authors: Barnaby Martin and Jos Martin

Published in: Dagstuhl Seminar Proceedings, Volume 9441, The Constraint Satisfaction Problem: Complexity and Approximability (2010)

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.

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Barnaby Martin and Jos Martin. The complexity of positive first-order logic without equality II: The four-element case. In The Constraint Satisfaction Problem: Complexity and Approximability. Dagstuhl Seminar Proceedings, Volume 9441, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{martin_et_al:DagSemProc.09441.5,
  author =	{Martin, Barnaby and Martin, Jos},
  title =	{{The complexity of positive first-order logic without equality II: The four-element case}},
  booktitle =	{The Constraint Satisfaction Problem: Complexity and Approximability},
  pages =	{1--12},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9441},
  editor =	{Andrei A. Bulatov and Martin Grohe and Phokion G. Kolaitis and Andrei Krokhin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09441.5},
  URN =		{urn:nbn:de:0030-drops-23670},
  doi =		{10.4230/DagSemProc.09441.5},
  annote =	{Keywords: Quantified constraints, Galois connection}
}

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

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