38 research outputs found
Answering Conjunctive Queries under Updates
We consider the task of enumerating and counting answers to -ary
conjunctive queries against relational databases that may be updated by
inserting or deleting tuples. We exhibit a new notion of q-hierarchical
conjunctive queries and show that these can be maintained efficiently in the
following sense. During a linear time preprocessing phase, we can build a data
structure that enables constant delay enumeration of the query results; and
when the database is updated, we can update the data structure and restart the
enumeration phase within constant time. For the special case of self-join free
conjunctive queries we obtain a dichotomy: if a query is not q-hierarchical,
then query enumeration with sublinear delay and sublinear update time
(and arbitrary preprocessing time) is impossible.
For answering Boolean conjunctive queries and for the more general problem of
counting the number of solutions of k-ary queries we obtain complete
dichotomies: if the query's homomorphic core is q-hierarchical, then size of
the the query result can be computed in linear time and maintained with
constant update time. Otherwise, the size of the query result cannot be
maintained with sublinear update time. All our lower bounds rely on the
OMv-conjecture, a conjecture on the hardness of online matrix-vector
multiplication that has recently emerged in the field of fine-grained
complexity to characterise the hardness of dynamic problems. The lower bound
for the counting problem additionally relies on the orthogonal vectors
conjecture, which in turn is implied by the strong exponential time hypothesis.
By sublinear we mean for some
, where is the size of the active domain of the current
database
Synchronization of organ pipes: experimental observations and modeling
We report measurements on the synchronization properties of organ pipes.
First, we investigate influence of an external acoustical signal from a
loudspeaker on the sound of an organ pipe. Second, the mutual influence of two
pipes with different pitch is analyzed. In analogy to the externally driven, or
mutually coupled self-sustained oscillators, one observes a frequency locking,
which can be explained by synchronization theory. Further, we measure the
dependence of the frequency of the signals emitted by two mutually detuned
pipes with varying distance between the pipes. The spectrum shows a broad
``hump'' structure, not found for coupled oscillators. This indicates a complex
coupling of the two organ pipes leading to nonlinear beat phenomena.Comment: 24 pages, 10 Figures, fully revised, 4 big figures separate in jpeg
format. accepted for Journal of the Acoustical Society of Americ
On insertion-deletion systems over relational words
We introduce a new notion of a relational word as a finite totally ordered
set of positions endowed with three binary relations that describe which
positions are labeled by equal data, by unequal data and those having an
undefined relation between their labels. We define the operations of insertion
and deletion on relational words generalizing corresponding operations on
strings. We prove that the transitive and reflexive closure of these operations
has a decidable membership problem for the case of short insertion-deletion
rules (of size two/three and three/two). At the same time, we show that in the
general case such systems can produce a coding of any recursively enumerable
language leading to undecidabilty of reachability questions.Comment: 24 pages, 8 figure
Composition with Target Constraints
It is known that the composition of schema mappings, each specified by
source-to-target tgds (st-tgds), can be specified by a second-order tgd (SO
tgd). We consider the question of what happens when target constraints are
allowed. Specifically, we consider the question of specifying the composition
of standard schema mappings (those specified by st-tgds, target egds, and a
weakly acyclic set of target tgds). We show that SO tgds, even with the
assistance of arbitrary source constraints and target constraints, cannot
specify in general the composition of two standard schema mappings. Therefore,
we introduce source-to-target second-order dependencies (st-SO dependencies),
which are similar to SO tgds, but allow equations in the conclusion. We show
that st-SO dependencies (along with target egds and target tgds) are sufficient
to express the composition of every finite sequence of standard schema
mappings, and further, every st-SO dependency specifies such a composition. In
addition to this expressive power, we show that st-SO dependencies enjoy other
desirable properties. In particular, they have a polynomial-time chase that
generates a universal solution. This universal solution can be used to find the
certain answers to unions of conjunctive queries in polynomial time. It is easy
to show that the composition of an arbitrary number of standard schema mappings
is equivalent to the composition of only two standard schema mappings. We show
that surprisingly, the analogous result holds also for schema mappings
specified by just st-tgds (no target constraints). This is proven by showing
that every SO tgd is equivalent to an unnested SO tgd (one where there is no
nesting of function symbols). Similarly, we prove unnesting results for st-SO
dependencies, with the same types of consequences.Comment: This paper is an extended version of: M. Arenas, R. Fagin, and A.
Nash. Composition with Target Constraints. In 13th International Conference
on Database Theory (ICDT), pages 129-142, 201
Dependency Tree Automata
Abstract. We introduce a new kind of tree automaton, a dependency tree automaton, that is suitable for deciding properties of classes of terms with binding. Two kinds of such automaton are defined, nondeterministic and alternating. We show that the nondeterministic automata have a decidable nonemptiness problem and leave as an open question whether this is true for the alternating version. The families of trees that both kinds recognise are closed under intersection and union. To illustrate the utility of the automata, we apply them to terms of simply typed lambda calculus and provide an automata-theoretic characterisation of solutions to the higher-order matching problem
Answering Non-Monotonic Queries in Relational Data Exchange
Relational data exchange is the problem of translating relational data from a
source schema into a target schema, according to a specification of the
relationship between the source data and the target data. One of the basic
issues is how to answer queries that are posed against target data. While
consensus has been reached on the definitive semantics for monotonic queries,
this issue turned out to be considerably more difficult for non-monotonic
queries. Several semantics for non-monotonic queries have been proposed in the
past few years. This article proposes a new semantics for non-monotonic
queries, called the GCWA*-semantics. It is inspired by semantics from the area
of deductive databases. We show that the GCWA*-semantics coincides with the
standard open world semantics on monotonic queries, and we further explore the
(data) complexity of evaluating non-monotonic queries under the
GCWA*-semantics. In particular, we introduce a class of schema mappings for
which universal queries can be evaluated under the GCWA*-semantics in
polynomial time (data complexity) on the core of the universal solutions.Comment: 55 pages, 3 figure
Cichlid biogeography: comment and review
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72313/1/j.1467-2979.2004.00148.x.pd
Molecular Phylogeny and Biogeography of the Native Rodents of Madagascar (Muridae: Nesomyinae): A Test of the Single-Origin Hypothesis
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72349/1/j.1096-0031.1999.tb00267.x.pd