3,905 research outputs found
Direct Access for Conjunctive Queries with Negation
Given a conjunctive query and a database , a direct access to
the answers of over is the operation of returning, given an
index , the answer for some order on its answers. While
this problem is -hard in general with respect to combined
complexity, many conjunctive queries have an underlying structure that allows
for a direct access to their answers for some lexicographical ordering that
takes polylogarithmic time in the size of the database after a polynomial time
precomputation. Previous work has precisely characterised the tractable classes
and given fine-grained lower bounds on the precomputation time needed depending
on the structure of the query.
In this paper, we generalise these tractability results to the case of signed
conjunctive queries, that is, conjunctive queries that may contain negative
atoms. Our technique is based on a class of circuits that can represent
relational data. We first show that this class supports tractable direct access
after a polynomial time preprocessing. We then give bounds on the size of the
circuit needed to represent the answer set of signed conjunctive queries
depending on their structure. Both results combined together allow us to prove
the tractability of direct access for a large class of conjunctive queries. On
the one hand, we recover the known tractable classes from the literature in the
case of positive conjunctive queries. On the other hand, we generalise and
unify known tractability results about negative conjunctive queries -- that is,
queries having only negated atoms. In particular, we show that the class of
-acyclic negative conjunctive queries and the class of bounded nest set
width negative conjunctive queries admit tractable direct access
Querying the Guarded Fragment
Evaluating a Boolean conjunctive query Q against a guarded first-order theory
F is equivalent to checking whether "F and not Q" is unsatisfiable. This
problem is relevant to the areas of database theory and description logic.
Since Q may not be guarded, well known results about the decidability,
complexity, and finite-model property of the guarded fragment do not obviously
carry over to conjunctive query answering over guarded theories, and had been
left open in general. By investigating finite guarded bisimilar covers of
hypergraphs and relational structures, and by substantially generalising
Rosati's finite chase, we prove for guarded theories F and (unions of)
conjunctive queries Q that (i) Q is true in each model of F iff Q is true in
each finite model of F and (ii) determining whether F implies Q is
2EXPTIME-complete. We further show the following results: (iii) the existence
of polynomial-size conformal covers of arbitrary hypergraphs; (iv) a new proof
of the finite model property of the clique-guarded fragment; (v) the small
model property of the guarded fragment with optimal bounds; (vi) a
polynomial-time solution to the canonisation problem modulo guarded
bisimulation, which yields (vii) a capturing result for guarded bisimulation
invariant PTIME.Comment: This is an improved and extended version of the paper of the same
title presented at LICS 201
On Low Treewidth Approximations of Conjunctive Queries
We recently initiated the study of approximations of conjunctive queries within classes that admit tractable query evaluation (with respect to combined complexity). Those include classes of acyclic, bounded treewidth, or bounded hypertreewidth queries. Such approximations are always guaranteed to exist. However, while for acyclic and bounded hypertreewidth queries we have shown a number of examples of interesting approximations, for queries of bounded treewidth the study had been restricted to queries over graphs, where such approximations usually trivialize. In this note we show that for relations of arity greater than two, the notion of low treewidth approximations is a rich one, as many queries possess them. In fact we look at approximations of queries of maximum possible treewidth by queries of minimum possible treewidth (i.e., one), and show that even in this case the structure of approximations remain rather rich as long as input relations are not binary
Tree-width for first order formulae
We introduce tree-width for first order formulae \phi, fotw(\phi). We show
that computing fotw is fixed-parameter tractable with parameter fotw. Moreover,
we show that on classes of formulae of bounded fotw, model checking is fixed
parameter tractable, with parameter the length of the formula. This is done by
translating a formula \phi\ with fotw(\phi)<k into a formula of the k-variable
fragment L^k of first order logic. For fixed k, the question whether a given
first order formula is equivalent to an L^k formula is undecidable. In
contrast, the classes of first order formulae with bounded fotw are fragments
of first order logic for which the equivalence is decidable.
Our notion of tree-width generalises tree-width of conjunctive queries to
arbitrary formulae of first order logic by taking into account the quantifier
interaction in a formula. Moreover, it is more powerful than the notion of
elimination-width of quantified constraint formulae, defined by Chen and Dalmau
(CSL 2005): for quantified constraint formulae, both bounded elimination-width
and bounded fotw allow for model checking in polynomial time. We prove that
fotw of a quantified constraint formula \phi\ is bounded by the
elimination-width of \phi, and we exhibit a class of quantified constraint
formulae with bounded fotw, that has unbounded elimination-width. A similar
comparison holds for strict tree-width of non-recursive stratified datalog as
defined by Flum, Frick, and Grohe (JACM 49, 2002).
Finally, we show that fotw has a characterization in terms of a cops and
robbers game without monotonicity cost
Logics for Unranked Trees: An Overview
Labeled unranked trees are used as a model of XML documents, and logical
languages for them have been studied actively over the past several years. Such
logics have different purposes: some are better suited for extracting data,
some for expressing navigational properties, and some make it easy to relate
complex properties of trees to the existence of tree automata for those
properties. Furthermore, logics differ significantly in their model-checking
properties, their automata models, and their behavior on ordered and unordered
trees. In this paper we present a survey of logics for unranked trees
Converging to the Chase - a Tool for Finite Controllability
We solve a problem, stated in [CGP10], showing that Sticky Datalog, defined
in the cited paper as an element of the Datalog\pm project, has the finite
controllability property. In order to do that, we develop a technique, which we
believe can have further applications, of approximating Chase(D, T), for a
database instance D and some sets of tuple generating dependencies T, by an
infinite sequence of finite structures, all of them being models of T
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