Exponential lower bounds and separation for query rewriting

Authors:
Stanislav Kikot;Roman Kontchakov;Vladimir Podolskii;Michael Zakharyaschev
Affiliations:
Department of Computer Science and Information Systems, Birkbeck, University of London, UK;Department of Computer Science and Information Systems, Birkbeck, University of London, UK;Steklov Mathematical Institute, Moscow, Russia;Department of Computer Science and Information Systems, Birkbeck, University of London, UK
Venue:
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Year:
2012

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Abstract

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.