857 research outputs found
Adding Logical Operators to Tree Pattern Queries on Graph-Structured Data
As data are increasingly modeled as graphs for expressing complex
relationships, the tree pattern query on graph-structured data becomes an
important type of queries in real-world applications. Most practical query
languages, such as XQuery and SPARQL, support logical expressions using
logical-AND/OR/NOT operators to define structural constraints of tree patterns.
In this paper, (1) we propose generalized tree pattern queries (GTPQs) over
graph-structured data, which fully support propositional logic of structural
constraints. (2) We make a thorough study of fundamental problems including
satisfiability, containment and minimization, and analyze the computational
complexity and the decision procedures of these problems. (3) We propose a
compact graph representation of intermediate results and a pruning approach to
reduce the size of intermediate results and the number of join operations --
two factors that often impair the efficiency of traditional algorithms for
evaluating tree pattern queries. (4) We present an efficient algorithm for
evaluating GTPQs using 3-hop as the underlying reachability index. (5)
Experiments on both real-life and synthetic data sets demonstrate the
effectiveness and efficiency of our algorithm, from several times to orders of
magnitude faster than state-of-the-art algorithms in terms of evaluation time,
even for traditional tree pattern queries with only conjunctive operations.Comment: 16 page
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
Evaluating Datalog via Tree Automata and Cycluits
We investigate parameterizations of both database instances and queries that
make query evaluation fixed-parameter tractable in combined complexity. We show
that clique-frontier-guarded Datalog with stratified negation (CFG-Datalog)
enjoys bilinear-time evaluation on structures of bounded treewidth for programs
of bounded rule size. Such programs capture in particular conjunctive queries
with simplicial decompositions of bounded width, guarded negation fragment
queries of bounded CQ-rank, or two-way regular path queries. Our result is
shown by translating to alternating two-way automata, whose semantics is
defined via cyclic provenance circuits (cycluits) that can be tractably
evaluated.Comment: 56 pages, 63 references. Journal version of "Combined Tractability of
Query Evaluation via Tree Automata and Cycluits (Extended Version)" at
arXiv:1612.04203. Up to the stylesheet, page/environment numbering, and
possible minor publisher-induced changes, this is the exact content of the
journal paper that will appear in Theory of Computing Systems. Update wrt
version 1: latest reviewer feedbac
Queries with Guarded Negation (full version)
A well-established and fundamental insight in database theory is that
negation (also known as complementation) tends to make queries difficult to
process and difficult to reason about. Many basic problems are decidable and
admit practical algorithms in the case of unions of conjunctive queries, but
become difficult or even undecidable when queries are allowed to contain
negation. Inspired by recent results in finite model theory, we consider a
restricted form of negation, guarded negation. We introduce a fragment of SQL,
called GN-SQL, as well as a fragment of Datalog with stratified negation,
called GN-Datalog, that allow only guarded negation, and we show that these
query languages are computationally well behaved, in terms of testing query
containment, query evaluation, open-world query answering, and boundedness.
GN-SQL and GN-Datalog subsume a number of well known query languages and
constraint languages, such as unions of conjunctive queries, monadic Datalog,
and frontier-guarded tgds. In addition, an analysis of standard benchmark
workloads shows that most usage of negation in SQL in practice is guarded
negation
Conjunctive Query Answering for the Description Logic SHIQ
Conjunctive queries play an important role as an expressive query language
for Description Logics (DLs). Although modern DLs usually provide for
transitive roles, conjunctive query answering over DL knowledge bases is only
poorly understood if transitive roles are admitted in the query. In this paper,
we consider unions of conjunctive queries over knowledge bases formulated in
the prominent DL SHIQ and allow transitive roles in both the query and the
knowledge base. We show decidability of query answering in this setting and
establish two tight complexity bounds: regarding combined complexity, we prove
that there is a deterministic algorithm for query answering that needs time
single exponential in the size of the KB and double exponential in the size of
the query, which is optimal. Regarding data complexity, we prove containment in
co-NP
Eliminating Recursion from Monadic Datalog Programs on Trees
We study the problem of eliminating recursion from monadic datalog programs
on trees with an infinite set of labels. We show that the boundedness problem,
i.e., determining whether a datalog program is equivalent to some nonrecursive
one is undecidable but the decidability is regained if the descendant relation
is disallowed. Under similar restrictions we obtain decidability of the problem
of equivalence to a given nonrecursive program. We investigate the connection
between these two problems in more detail
Querying the Unary Negation Fragment with Regular Path Expressions
The unary negation fragment of first-order logic (UNFO) has recently been proposed as a generalization of modal logic that shares many of its good computational and model-theoretic properties. It is attractive from the perspective of database theory because it can express conjunctive queries (CQs) and ontologies formulated in many description logics (DLs). Both are relevant for ontology-mediated querying and, in fact, CQ evaluation under UNFO ontologies (and thus also under DL ontologies) can be `expressed\u27 in UNFO as a satisfiability problem. In this paper, we consider the natural extension of UNFO with regular expressions on binary relations. The resulting logic UNFOreg can express (unions of) conjunctive two-way regular path queries (C2RPQs) and ontologies formulated in DLs that include transitive roles and regular expressions on roles. Our main results are that evaluating C2RPQs under UNFOreg ontologies is decidable, 2ExpTime-complete in combined complexity, and coNP-complete in data complexity, and that satisfiability in UNFOreg is 2ExpTime-complete, thus not harder than in UNFO
Reasoning with Individuals for the Description Logic SHIQ
While there has been a great deal of work on the development of reasoning
algorithms for expressive description logics, in most cases only Tbox reasoning
is considered. In this paper we present an algorithm for combined Tbox and Abox
reasoning in the SHIQ description logic. This algorithm is of particular
interest as it can be used to decide the problem of (database) conjunctive
query containment w.r.t. a schema. Moreover, the realisation of an efficient
implementation should be relatively straightforward as it can be based on an
existing highly optimised implementation of the Tbox algorithm in the FaCT
system.Comment: To appear at CADE-1
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