152,081 research outputs found
A Trichotomy for Regular Simple Path Queries on Graphs
Regular path queries (RPQs) select nodes connected by some path in a graph.
The edge labels of such a path have to form a word that matches a given regular
expression. We investigate the evaluation of RPQs with an additional constraint
that prevents multiple traversals of the same nodes. Those regular simple path
queries (RSPQs) find several applications in practice, yet they quickly become
intractable, even for basic languages such as (aa)* or a*ba*.
In this paper, we establish a comprehensive classification of regular
languages with respect to the complexity of the corresponding regular simple
path query problem. More precisely, we identify the fragment that is maximal in
the following sense: regular simple path queries can be evaluated in polynomial
time for every regular language L that belongs to this fragment and evaluation
is NP-complete for languages outside this fragment. We thus fully characterize
the frontier between tractability and intractability for RSPQs, and we refine
our results to show the following trichotomy: Evaluations of RSPQs is either
AC0, NL-complete or NP-complete in data complexity, depending on the regular
language L. The fragment identified also admits a simple characterization in
terms of regular expressions.
Finally, we also discuss the complexity of the following decision problem:
decide, given a language L, whether finding a regular simple path for L is
tractable. We consider several alternative representations of L: DFAs, NFAs or
regular expressions, and prove that this problem is NL-complete for the first
representation and PSPACE-complete for the other two. As a conclusion we extend
our results from edge-labeled graphs to vertex-labeled graphs and vertex-edge
labeled graphs.Comment: 15 pages, conference submissio
Regular expressions as violin bowing patterns
String players spend a significant amount of practice time creating and learning bowings. These may be indicated in the music using up-bow and down-bow symbols, but those traditional notations do not capture the complex bowing patterns that are latent within the music. Regular expressions, a mathematical notation for a simple class of formal languages, can describe precisely the bowing patterns that commonly arise in string music. A software tool based on regular expressions enables performers to search for passages that can be handled with similar bowings, and to edit them consistently. A computer-based music editor incorporating bowing patterns has been implemented, using Lilypond to typeset the music. Our approach has been evaluated by using the editor to study ten movements from six violin sonatas by W. A. Mozart. Our experience shows that the editor is successful at finding passages and inserting bowings; that relatively complex patterns occur a number of times; and that the bowings can be inserted automatically and consistently
Two-variable first order logic with modular predicates over words
We consider first order formulae over the signature consisting of the symbols of the alphabet, the symbol < (interpreted as a linear order) and the set MOD of modular numerical predicates. We study the expressive power of FO 2 [<, MOD], the two-variable first order logic over this signature, interpreted over finite words. We give an algebraic characterization of the corresponding regular languages in terms of their syntactic morphisms and we also give simple unambiguous regular expressions for them. It follows that one can decide whether a given regular language is captured by FO 2 [<, MOD]. Our proofs rely on a combination of arguments from semigroup theory (stamps), model theory (Ehrenfeucht-Fraïssé games) and combinatorics
McRunjob: A High Energy Physics Workflow Planner for Grid Production Processing
McRunjob is a powerful grid workflow manager used to manage the generation of
large numbers of production processing jobs in High Energy Physics. In use at
both the DZero and CMS experiments, McRunjob has been used to manage large
Monte Carlo production processing since 1999 and is being extended to uses in
regular production processing for analysis and reconstruction. Described at
CHEP 2001, McRunjob converts core metadata into jobs submittable in a variety
of environments. The powerful core metadata description language includes
methods for converting the metadata into persistent forms, job descriptions,
multi-step workflows, and data provenance information. The language features
allow for structure in the metadata by including full expressions, namespaces,
functional dependencies, site specific parameters in a grid environment, and
ontological definitions. It also has simple control structures for
parallelization of large jobs. McRunjob features a modular design which allows
for easy expansion to new job description languages or new application level
tasks.Comment: CHEP 2003 serial number TUCT00
Answering SPARQL queries modulo RDF Schema with paths
SPARQL is the standard query language for RDF graphs. In its strict
instantiation, it only offers querying according to the RDF semantics and would
thus ignore the semantics of data expressed with respect to (RDF) schemas or
(OWL) ontologies. Several extensions to SPARQL have been proposed to query RDF
data modulo RDFS, i.e., interpreting the query with RDFS semantics and/or
considering external ontologies. We introduce a general framework which allows
for expressing query answering modulo a particular semantics in an homogeneous
way. In this paper, we discuss extensions of SPARQL that use regular
expressions to navigate RDF graphs and may be used to answer queries
considering RDFS semantics. We also consider their embedding as extensions of
SPARQL. These SPARQL extensions are interpreted within the proposed framework
and their drawbacks are presented. In particular, we show that the PSPARQL
query language, a strict extension of SPARQL offering transitive closure,
allows for answering SPARQL queries modulo RDFS graphs with the same complexity
as SPARQL through a simple transformation of the queries. We also consider
languages which, in addition to paths, provide constraints. In particular, we
present and compare nSPARQL and our proposal CPSPARQL. We show that CPSPARQL is
expressive enough to answer full SPARQL queries modulo RDFS. Finally, we
compare the expressiveness and complexity of both nSPARQL and the corresponding
fragment of CPSPARQL, that we call cpSPARQL. We show that both languages have
the same complexity through cpSPARQL, being a proper extension of SPARQL graph
patterns, is more expressive than nSPARQL.Comment: RR-8394; alkhateeb2003
A survey of parallel execution strategies for transitive closure and logic programs
An important feature of database technology of the nineties is the use of parallelism for speeding up the execution of complex queries. This technology is being tested in several experimental database architectures and a few commercial systems for conventional select-project-join queries. In particular, hash-based fragmentation is used to distribute data to disks under the control of different processors in order to perform selections and joins in parallel. With the development of new query languages, and in particular with the definition of transitive closure queries and of more general logic programming queries, the new dimension of recursion has been added to query processing. Recursive queries are complex; at the same time, their regular structure is particularly suited for parallel execution, and parallelism may give a high efficiency gain. We survey the approaches to parallel execution of recursive queries that have been presented in the recent literature. We observe that research on parallel execution of recursive queries is separated into two distinct subareas, one focused on the transitive closure of Relational Algebra expressions, the other one focused on optimization of more general Datalog queries. Though the subareas seem radically different because of the approach and formalism used, they have many common features. This is not surprising, because most typical Datalog queries can be solved by means of the transitive closure of simple algebraic expressions. We first analyze the relationship between the transitive closure of expressions in Relational Algebra and Datalog programs. We then review sequential methods for evaluating transitive closure, distinguishing iterative and direct methods. We address the parallelization of these methods, by discussing various forms of parallelization. Data fragmentation plays an important role in obtaining parallel execution; we describe hash-based and semantic fragmentation. Finally, we consider Datalog queries, and present general methods for parallel rule execution; we recognize the similarities between these methods and the methods reviewed previously, when the former are applied to linear Datalog queries. We also provide a quantitative analysis that shows the impact of the initial data distribution on the performance of methods
A Perfect Match for Reasoning, Explanation, and Reason Maintenance
Path query languages have been previously shown to com-
plement RDF rule languages in a natural way and have been used as
a means to implement the RDFS derivation rules. RPL is a novel path
query language specifically designed to be incorporated with RDF rules
and comes in three
avors: Node-, edge- and path-
avored expressions
allow to express conditional regular expressions over the nodes, edges, or
nodes and edges appearing on paths within RDF graphs. Providing reg-
ular string expressions and negation, RPL is more expressive than other
RDF path languages that have been proposed. We give a compositional
semantics for RPL and show that it can be evaluated efficiently, while
several possible extensions of it cannot
A Trichotomy for Regular Trail Queries
Regular path queries (RPQs) are an essential component of graph query languages. Such queries consider a regular expression r and a directed edge-labeled graph G and search for paths in G for which the sequence of labels is in the language of r. In order to avoid having to consider infinitely many paths, some database engines restrict such paths to be trails, that is, they only consider paths without repeated edges. In this paper we consider the evaluation problem for RPQs under trail semantics, in the case where the expression is fixed. We show that, in this setting, there exists a trichotomy. More precisely, the complexity of RPQ evaluation divides the regular languages into the finite languages, the class T_tract (for which the problem is tractable), and the rest. Interestingly, the tractable class in the trichotomy is larger than for the trichotomy for simple paths, discovered by Bagan et al. [Bagan et al., 2013]. In addition to this trichotomy result, we also study characterizations of the tractable class, its expressivity, the recognition problem, closure properties, and show how the decision problem can be extended to the enumeration problem, which is relevant to practice
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