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

Martin, Barnaby and Martin, Jos (2010) The complexity of positive first-order logic without equality II: the four-element case. Computer Science Logic. In: 24th International Workshop (CSL 2010), 19th Annual Conference of the EACSL, 23-27 August 2010, Brno, Czech Republic. ISBN 9783642152047. ISSN 0302-9743 [Conference or Workshop Item] (doi:10.1007/978-3-642-15205-4_33)

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 Pspace-complete.

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