4,900 research outputs found
On Chase Termination Beyond Stratification
We study the termination problem of the chase algorithm, a central tool in
various database problems such as the constraint implication problem,
Conjunctive Query optimization, rewriting queries using views, data exchange,
and data integration. The basic idea of the chase is, given a database instance
and a set of constraints as input, to fix constraint violations in the database
instance. It is well-known that, for an arbitrary set of constraints, the chase
does not necessarily terminate (in general, it is even undecidable if it does
or not). Addressing this issue, we review the limitations of existing
sufficient termination conditions for the chase and develop new techniques that
allow us to establish weaker sufficient conditions. In particular, we introduce
two novel termination conditions called safety and inductive restriction, and
use them to define the so-called T-hierarchy of termination conditions. We then
study the interrelations of our termination conditions with previous conditions
and the complexity of checking our conditions. This analysis leads to an
algorithm that checks membership in a level of the T-hierarchy and accounts for
the complexity of termination conditions. As another contribution, we study the
problem of data-dependent chase termination and present sufficient termination
conditions w.r.t. fixed instances. They might guarantee termination although
the chase does not terminate in the general case. As an application of our
techniques beyond those already mentioned, we transfer our results into the
field of query answering over knowledge bases where the chase on the underlying
database may not terminate, making existing algorithms applicable to broader
classes of constraints.Comment: Technical Report of VLDB 2009 conference versio
The data-exchange chase under the microscope
In this paper we take closer look at recent developments for the chase
procedure, and provide additional results. Our analysis allows us create a
taxonomy of the chase variations and the properties they satisfy. Two of the
most central problems regarding the chase is termination, and discovery of
restricted classes of sets of dependencies that guarantee termination of the
chase. The search for the restricted classes has been motivated by a fairly
recent result that shows that it is undecidable to determine whether the chase
with a given dependency set will terminate on a given instance. There is a
small dissonance here, since the quest has been for classes of sets of
dependencies guaranteeing termination of the chase on all instances, even
though the latter problem was not known to be undecidable. We resolve the
dissonance in this paper by showing that determining whether the chase with a
given set of dependencies terminates on all instances is coRE-complete. For the
hardness proof we use a reduction from word rewriting systems, thereby also
showing the close connection between the chase and word rewriting. The same
reduction also gives us the aforementioned instance-dependent RE-completeness
result as a byproduct. For one of the restricted classes guaranteeing
termination on all instances, the stratified sets dependencies, we provide new
complexity results for the problem of testing whether a given set of
dependencies belongs to it. These results rectify some previous claims that
have occurred in the literature.Comment: arXiv admin note: substantial text overlap with arXiv:1303.668
Foundations of SPARQL Query Optimization
The SPARQL query language is a recent W3C standard for processing RDF data, a
format that has been developed to encode information in a machine-readable way.
We investigate the foundations of SPARQL query optimization and (a) provide
novel complexity results for the SPARQL evaluation problem, showing that the
main source of complexity is operator OPTIONAL alone; (b) propose a
comprehensive set of algebraic query rewriting rules; (c) present a framework
for constraint-based SPARQL optimization based upon the well-known chase
procedure for Conjunctive Query minimization. In this line, we develop two
novel termination conditions for the chase. They subsume the strongest
conditions known so far and do not increase the complexity of the recognition
problem, thus making a larger class of both Conjunctive and SPARQL queries
amenable to constraint-based optimization. Our results are of immediate
practical interest and might empower any SPARQL query optimizer
Evaluation of an Early Classic Round Structure at Santa Rita Corozal, Belize
Round structures in the Maya area are an architectural form that is not well understood, in part due to the relatively few examples recovered through archaeological excavations. The site of Santa Rita Corozal, Belize offers one of the few examples of an Early Classic Period round structure (Structure 135) in the Maya region, one that is distinctive in its timing and architectural form. This thesis seeks to compare Structure 135 with the patterns of round structures identified in the Preclassic and Terminal/early Postclassic Periods, when there are comparatively more examples and to pinpoint the multiple construction periods evidenced in the excavations to define the changes to the structure over time. Based on this research, Structure 135 at Santa Rita Corozal does not clearly conform to earlier or later patterns of round structures in the Maya region and its use before abandonment and eventual transformation to a rectilinear shape was shorter than previously thought. This research also offers insights into the need for the contextual analysis of ceramics, and the difficulties of assuming context through the use of construction fill, even with a clear cultural formation process
Detecting Decidable Classes of Finitely Ground Logic Programs with Function Symbols
In this article, we propose a new technique for checking whether the bottom-up evaluation of logic programs with function symbols terminates. The technique is based on the definition of
mappings
from arguments to strings of function symbols, representing possible values which could be taken by arguments during the bottom-up evaluation. Starting from mappings, we identify
mapping-restricted
arguments, a subset of limited arguments, namely arguments that take values from finite domains. Mapping-restricted programs, consisting of rules whose arguments are all mapping restricted, are terminating under the bottom-up computation, as all of its arguments take values from finite domains. We show that mappings can be computed by transforming the original program into a unary logic program: this allows us to establish decidability of checking if a program is mapping restricted. We study the complexity of the presented approach and compare it to other techniques known in the literature. We also introduce an extension of the proposed approach that is able to recognize a wider class of logic programs. The presented technique provides a significant improvement, as it can detect terminating programs not identified by other criteria proposed so far. Furthermore, it can be combined with other techniques to further enlarge the class of programs recognized as terminating under the bottom-up evaluation.
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