1,427 research outputs found
On (in)tractability of OBDA with OWL 2 QL
We show that, although conjunctive queries over OWL 2 QL ontologies are reducible to database queries, no algorithm can construct such a reduction in polynomial time without changing the data. On the other hand, we give a polynomial reduction for OWL2QL ontologies without role inclusions
The tractability frontier of well-designed SPARQL queries
We study the complexity of query evaluation of SPARQL queries. We focus on
the fundamental fragment of well-designed SPARQL restricted to the AND,
OPTIONAL and UNION operators. Our main result is a structural characterisation
of the classes of well-designed queries that can be evaluated in polynomial
time. In particular, we introduce a new notion of width called domination
width, which relies on the well-known notion of treewidth. We show that, under
some complexity theoretic assumptions, the classes of well-designed queries
that can be evaluated in polynomial time are precisely those of bounded
domination width
Capturing Polynomial Time using Modular Decomposition
The question of whether there is a logic that captures polynomial time is one
of the main open problems in descriptive complexity theory and database theory.
In 2010 Grohe showed that fixed point logic with counting captures polynomial
time on all classes of graphs with excluded minors. We now consider classes of
graphs with excluded induced subgraphs. For such graph classes, an effective
graph decomposition, called modular decomposition, was introduced by Gallai in
1976. The graphs that are non-decomposable with respect to modular
decomposition are called prime. We present a tool, the Modular Decomposition
Theorem, that reduces (definable) canonization of a graph class C to
(definable) canonization of the class of prime graphs of C that are colored
with binary relations on a linearly ordered set. By an application of the
Modular Decomposition Theorem, we show that fixed point logic with counting
captures polynomial time on the class of permutation graphs. Within the proof
of the Modular Decomposition Theorem, we show that the modular decomposition of
a graph is definable in symmetric transitive closure logic with counting. We
obtain that the modular decomposition tree is computable in logarithmic space.
It follows that cograph recognition and cograph canonization is computable in
logarithmic space.Comment: 38 pages, 10 Figures. A preliminary version of this article appeared
in the Proceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer
Science (LICS '17
The Arity Hierarchy in the Polyadic -Calculus
The polyadic mu-calculus is a modal fixpoint logic whose formulas define
relations of nodes rather than just sets in labelled transition systems. It can
express exactly the polynomial-time computable and bisimulation-invariant
queries on finite graphs. In this paper we show a hierarchy result with respect
to expressive power inside the polyadic mu-calculus: for every level of
fixpoint alternation, greater arity of relations gives rise to higher
expressive power. The proof uses a diagonalisation argument.Comment: In Proceedings FICS 2015, arXiv:1509.0282
The parameterized space complexity of model-checking bounded variable first-order logic
The parameterized model-checking problem for a class of first-order sentences
(queries) asks to decide whether a given sentence from the class holds true in
a given relational structure (database); the parameter is the length of the
sentence. We study the parameterized space complexity of the model-checking
problem for queries with a bounded number of variables. For each bound on the
quantifier alternation rank the problem becomes complete for the corresponding
level of what we call the tree hierarchy, a hierarchy of parameterized
complexity classes defined via space bounded alternating machines between
parameterized logarithmic space and fixed-parameter tractable time. We observe
that a parameterized logarithmic space model-checker for existential bounded
variable queries would allow to improve Savitch's classical simulation of
nondeterministic logarithmic space in deterministic space .
Further, we define a highly space efficient model-checker for queries with a
bounded number of variables and bounded quantifier alternation rank. We study
its optimality under the assumption that Savitch's Theorem is optimal
The complexity of acyclic conjunctive queries revisited
In this paper, we consider first-order logic over unary functions and study
the complexity of the evaluation problem for conjunctive queries described by
such kind of formulas. A natural notion of query acyclicity for this language
is introduced and we study the complexity of a large number of variants or
generalizations of acyclic query problems in that context (Boolean or not
Boolean, with or without inequalities, comparisons, etc...). Our main results
show that all those problems are \textit{fixed-parameter linear} i.e. they can
be evaluated in time where is the
size of the query , the database size, is
the size of the output and is some function whose value depends on the
specific variant of the query problem (in some cases, is the identity
function). Our results have two kinds of consequences. First, they can be
easily translated in the relational (i.e., classical) setting. Previously known
bounds for some query problems are improved and new tractable cases are then
exhibited. Among others, as an immediate corollary, we improve a result of
\~\cite{PapadimitriouY-99} by showing that any (relational) acyclic conjunctive
query with inequalities can be evaluated in time
. A second consequence of our method is
that it provides a very natural descriptive approach to the complexity of
well-known algorithmic problems. A number of examples (such as acyclic subgraph
problems, multidimensional matching, etc...) are considered for which new
insights of their complexity are given.Comment: 30 page
Reflective Relational Machines
AbstractWe propose a model of database programming withreflection(dynamic generation of queries within the host programming language), called thereflective relational machine, and characterize the power of this machine in terms of known complexity classes. In particular, the polynomial time restriction of the reflective relational machine is shown to express PSPACE, and to correspond precisely to uniform circuits of polynomial depth and exponential size. This provides an alternative, logic based formulation of the uniform circuit model, which may be more convenient for problems naturally formulated in logic terms, and establishes that reflection allows for more “intense” parallelism, which is not attainable otherwise (unless P=PSPACE). We also explore the power of the reflective relational machine subject to restrictions on the number of variables used, emphasizing the case of sublinear bounds
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