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

Authors:
Barnaby Martin;Jos Martin
Affiliations:
School of Engineering and Computing Sciences, Durham University, Durham, U.K.;The MathWorks, Cambridge, U.K.
Venue:
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Year:
2010

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Abstract

We study the complexity of evaluating positive equality-free sentences of first-order 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 L, is NP-complete, is co-NP-complete or is Pspacecomplete.