We establish connections between the size of circuits and formulas computing monotone Boolean functions and the size of first-order and nonrecursive Datalog rewritings for conjunctive queries over OWL 2 QL ontologies. We use known lower bounds and separation results from circuit complexity to prove similar results for the size of rewritings that do not use non-signature constants. For example, we show that, in the worst case, positive existential and nonrecursive Datalog rewritings are exponentially longer than the original queries; nonrecursive Datalog rewritings are in general exponentially more succinct than positive existential rewritings; while first-order rewritings can be superpolynomially more succinct than positive existential rewritings.
@article{arxiv.1202.4193,
title = {Exponential Lower Bounds and Separation for Query Rewriting},
author = {Stanislav Kikot and Roman Kontchakov and Vladimir Podolskii and Michael Zakharyaschev},
journal= {arXiv preprint arXiv:1202.4193},
year = {2012}
}