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

Authors Barnaby Martin, Jos Martin



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Barnaby Martin
Jos Martin

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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)
https://doi.org/10.4230/DagSemProc.09441.5

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.
Keywords
  • Quantified constraints
  • Galois connection

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