9,438 research outputs found
The equational theory of the natural join and inner union is decidable
The natural join and the inner union operations combine relations of a
database. Tropashko and Spight [24] realized that these two operations are the
meet and join operations in a class of lattices, known by now as the relational
lattices. They proposed then lattice theory as an algebraic approach to the
theory of databases, alternative to the relational algebra. Previous works [17,
22] proved that the quasiequational theory of these lattices-that is, the set
of definite Horn sentences valid in all the relational lattices-is undecidable,
even when the signature is restricted to the pure lattice signature. We prove
here that the equational theory of relational lattices is decidable. That, is
we provide an algorithm to decide if two lattice theoretic terms t, s are made
equal under all intepretations in some relational lattice. We achieve this goal
by showing that if an inclusion t s fails in any of these lattices, then
it fails in a relational lattice whose size is bound by a triple exponential
function of the sizes of t and s.Comment: arXiv admin note: text overlap with arXiv:1607.0298
On tractability and congruence distributivity
Constraint languages that arise from finite algebras have recently been the
object of study, especially in connection with the Dichotomy Conjecture of
Feder and Vardi. An important class of algebras are those that generate
congruence distributive varieties and included among this class are lattices,
and more generally, those algebras that have near-unanimity term operations. An
algebra will generate a congruence distributive variety if and only if it has a
sequence of ternary term operations, called Jonsson terms, that satisfy certain
equations.
We prove that constraint languages consisting of relations that are invariant
under a short sequence of Jonsson terms are tractable by showing that such
languages have bounded relational width
Fast and Simple Relational Processing of Uncertain Data
This paper introduces U-relations, a succinct and purely relational
representation system for uncertain databases. U-relations support
attribute-level uncertainty using vertical partitioning. If we consider
positive relational algebra extended by an operation for computing possible
answers, a query on the logical level can be translated into, and evaluated as,
a single relational algebra query on the U-relation representation. The
translation scheme essentially preserves the size of the query in terms of
number of operations and, in particular, number of joins. Standard techniques
employed in off-the-shelf relational database management systems are effective
for optimizing and processing queries on U-relations. In our experiments we
show that query evaluation on U-relations scales to large amounts of data with
high degrees of uncertainty.Comment: 12 pages, 14 figure
Formal Representation of the SS-DB Benchmark and Experimental Evaluation in EXTASCID
Evaluating the performance of scientific data processing systems is a
difficult task considering the plethora of application-specific solutions
available in this landscape and the lack of a generally-accepted benchmark. The
dual structure of scientific data coupled with the complex nature of processing
complicate the evaluation procedure further. SS-DB is the first attempt to
define a general benchmark for complex scientific processing over raw and
derived data. It fails to draw sufficient attention though because of the
ambiguous plain language specification and the extraordinary SciDB results. In
this paper, we remedy the shortcomings of the original SS-DB specification by
providing a formal representation in terms of ArrayQL algebra operators and
ArrayQL/SciQL constructs. These are the first formal representations of the
SS-DB benchmark. Starting from the formal representation, we give a reference
implementation and present benchmark results in EXTASCID, a novel system for
scientific data processing. EXTASCID is complete in providing native support
both for array and relational data and extensible in executing any user code
inside the system by the means of a configurable metaoperator. These features
result in an order of magnitude improvement over SciDB at data loading,
extracting derived data, and operations over derived data.Comment: 32 pages, 3 figure
A Survey on Array Storage, Query Languages, and Systems
Since scientific investigation is one of the most important providers of
massive amounts of ordered data, there is a renewed interest in array data
processing in the context of Big Data. To the best of our knowledge, a unified
resource that summarizes and analyzes array processing research over its long
existence is currently missing. In this survey, we provide a guide for past,
present, and future research in array processing. The survey is organized along
three main topics. Array storage discusses all the aspects related to array
partitioning into chunks. The identification of a reduced set of array
operators to form the foundation for an array query language is analyzed across
multiple such proposals. Lastly, we survey real systems for array processing.
The result is a thorough survey on array data storage and processing that
should be consulted by anyone interested in this research topic, independent of
experience level. The survey is not complete though. We greatly appreciate
pointers towards any work we might have forgotten to mention.Comment: 44 page
Taylor's modularity conjecture and related problems for idempotent varieties
We provide a partial result on Taylor's modularity conjecture, and several
related problems. Namely, we show that the interpretability join of two
idempotent varieties that are not congruence modular is not congruence modular
either, and we prove an analogue for idempotent varieties with a cube term.
Also, similar results are proved for linear varieties and the properties of
congruence modularity, having a cube term, congruence -permutability for a
fixed , and satisfying a non-trivial congruence identity.Comment: 27 page
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