5,086 research outputs found
Provenance for Aggregate Queries
We study in this paper provenance information for queries with aggregation.
Provenance information was studied in the context of various query languages
that do not allow for aggregation, and recent work has suggested to capture
provenance by annotating the different database tuples with elements of a
commutative semiring and propagating the annotations through query evaluation.
We show that aggregate queries pose novel challenges rendering this approach
inapplicable. Consequently, we propose a new approach, where we annotate with
provenance information not just tuples but also the individual values within
tuples, using provenance to describe the values computation. We realize this
approach in a concrete construction, first for "simple" queries where the
aggregation operator is the last one applied, and then for arbitrary (positive)
relational algebra queries with aggregation; the latter queries are shown to be
more challenging in this context. Finally, we use aggregation to encode queries
with difference, and study the semantics obtained for such queries on
provenance annotated databases
On the Limitations of Provenance for Queries With Difference
The annotation of the results of database transformations was shown to be
very effective for various applications. Until recently, most works in this
context focused on positive query languages. The provenance semirings is a
particular approach that was proven effective for these languages, and it was
shown that when propagating provenance with semirings, the expected equivalence
axioms of the corresponding query languages are satisfied. There have been
several attempts to extend the framework to account for relational algebra
queries with difference. We show here that these suggestions fail to satisfy
some expected equivalence axioms (that in particular hold for queries on
"standard" set and bag databases). Interestingly, we show that this is not a
pitfall of these particular attempts, but rather every such attempt is bound to
fail in satisfying these axioms, for some semirings. Finally, we show
particular semirings for which an extension for supporting difference is
(im)possible.Comment: TAPP 201
Definability of linear equation systems over groups and rings
Motivated by the quest for a logic for PTIME and recent insights that the
descriptive complexity of problems from linear algebra is a crucial aspect of
this problem, we study the solvability of linear equation systems over finite
groups and rings from the viewpoint of logical (inter-)definability. All
problems that we consider are decidable in polynomial time, but not expressible
in fixed-point logic with counting. They also provide natural candidates for a
separation of polynomial time from rank logics, which extend fixed-point logics
by operators for determining the rank of definable matrices and which are
sufficient for solvability problems over fields. Based on the structure theory
of finite rings, we establish logical reductions among various solvability
problems. Our results indicate that all solvability problems for linear
equation systems that separate fixed-point logic with counting from PTIME can
be reduced to solvability over commutative rings. Moreover, we prove closure
properties for classes of queries that reduce to solvability over rings, which
provides normal forms for logics extended with solvability operators. We
conclude by studying the extent to which fixed-point logic with counting can
express problems in linear algebra over finite commutative rings, generalising
known results on the logical definability of linear-algebraic problems over
finite fields
Database queries and constraints via lifting problems
Previous work has demonstrated that categories are useful and expressive
models for databases. In the present paper we build on that model, showing that
certain queries and constraints correspond to lifting problems, as found in
modern approaches to algebraic topology. In our formulation, each so-called
SPARQL graph pattern query corresponds to a category-theoretic lifting problem,
whereby the set of solutions to the query is precisely the set of lifts. We
interpret constraints within the same formalism and then investigate some basic
properties of queries and constraints. In particular, to any database we
can associate a certain derived database \Qry(\pi) of queries on . As an
application, we explain how giving users access to certain parts of
\Qry(\pi), rather than direct access to , improves ones ability to
manage the impact of schema evolution
Resource modalities in game semantics
The description of resources in game semantics has never achieved the
simplicity and precision of linear logic, because of a misleading conception:
the belief that linear logic is more primitive than game semantics. We advocate
instead the contrary: that game semantics is conceptually more primitive than
linear logic. Starting from this revised point of view, we design a categorical
model of resources in game semantics, and construct an arena game model where
the usual notion of bracketing is extended to multi- bracketing in order to
capture various resource policies: linear, affine and exponential
Abstract structure of unitary oracles for quantum algorithms
We show that a pair of complementary dagger-Frobenius algebras, equipped with
a self-conjugate comonoid homomorphism onto one of the algebras, produce a
nontrivial unitary morphism on the product of the algebras. This gives an
abstract understanding of the structure of an oracle in a quantum computation,
and we apply this understanding to develop a new algorithm for the
deterministic identification of group homomorphisms into abelian groups. We
also discuss an application to the categorical theory of signal-flow networks.Comment: In Proceedings QPL 2014, arXiv:1412.810
Sharp Quantum vs. Classical Query Complexity Separations
We obtain the strongest separation between quantum and classical query
complexity known to date -- specifically, we define a black-box problem that
requires exponentially many queries in the classical bounded-error case, but
can be solved exactly in the quantum case with a single query (and a polynomial
number of auxiliary operations). The problem is simple to define and the
quantum algorithm solving it is also simple when described in terms of certain
quantum Fourier transforms (QFTs) that have natural properties with respect to
the algebraic structures of finite fields. These QFTs may be of independent
interest, and we also investigate generalizations of them to noncommutative
finite rings.Comment: 13 pages, change in title, improvements in presentation, and minor
corrections. To appear in Algorithmic
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