The complexity of positive first-order logic without equality
Logic in Computer Science
2010-03-04 v1 Computational Complexity
Abstract
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 non-uniform quantified constraint satisfaction problem QCSP(B). We introduce surjective hyper-endomorphisms 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 Logspace, is NP-complete, is co-NP-complete or is Pspace-complete.
Cite
@article{arxiv.1003.0802,
title = {The complexity of positive first-order logic without equality},
author = {Florent Madelaine and Barnaby Martin},
journal= {arXiv preprint arXiv:1003.0802},
year = {2010}
}