The complexity of positive first-order logic without equality

Madelaine, Florent and Martin, Barnaby (2012) The complexity of positive first-order logic without equality. ACM Transactions on Computational Logic (TOCL), 13 (1). ISSN 1529-3785 (doi:10.1145/2071368.2071373)

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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 nonuniform quantified constraint satisfaction problem QCSP(B). We introduce surjective hyper-endomorphisms and use them in proving a Galois connection that characterizes 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 either is in L, is NP-complete, is co-NP-complete, or is Pspace-complete.

Item Type: Article
Research Areas: A. > School of Science and Technology > Computer Science
A. > School of Science and Technology > Computer Science > Foundations of Computing group
Item ID: 9643
Depositing User: Devika Mohan
Date Deposited: 20 Dec 2012 10:45
Last Modified: 24 Apr 2018 14:12
URI: https://eprints.mdx.ac.uk/id/eprint/9643

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