The complexity of positive first-order logic without equality

We study the complexity of evaluating positive equality-free sentences of first-order (FO) logic over a fixed, finite structure B. This may be seen as a natural generalisation of the nonuniform quantified constraint satisfaction problem QCSP(B). We introduce surjective hyperendomorphisms and use them in proving a Galois connection that characterises definability in positive equality-free FO. Through an algebraic method, we derive a complete complexity classification for our problems as B ranges over structures of size at most three. Specifically, each problem is either in L, is NP-complete, is co-NP-complete or is Pspace-complete.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Florent R. Madelaine, Barnaby Martin
• Keywords: CORR 2010, Education, Nonuniform Quantified Constraint, Positive Equality-free Fo, Positive Equality-free Sentences