15 research outputs found
Relative Expressive Power of Navigational Querying on Graphs
Motivated by both established and new applications, we study navigational
query languages for graphs (binary relations). The simplest language has only
the two operators union and composition, together with the identity relation.
We make more powerful languages by adding any of the following operators:
intersection; set difference; projection; coprojection; converse; and the
diversity relation. All these operators map binary relations to binary
relations. We compare the expressive power of all resulting languages. We do
this not only for general path queries (queries where the result may be any
binary relation) but also for boolean or yes/no queries (expressed by the
nonemptiness of an expression). For both cases, we present the complete Hasse
diagram of relative expressiveness. In particular the Hasse diagram for boolean
queries contains some nontrivial separations and a few surprising collapses.Comment: An extended abstract announcing the results of this paper was
presented at the 14th International Conference on Database Theory, Uppsala,
Sweden, March 201
Context-Free Path Queries on RDF Graphs
Navigational graph queries are an important class of queries that canextract
implicit binary relations over the nodes of input graphs. Most of the
navigational query languages used in the RDF community, e.g. property paths in
W3C SPARQL 1.1 and nested regular expressions in nSPARQL, are based on the
regular expressions. It is known that regular expressions have limited
expressivity; for instance, some natural queries, like same generation-queries,
are not expressible with regular expressions. To overcome this limitation, in
this paper, we present cfSPARQL, an extension of SPARQL query language equipped
with context-free grammars. The cfSPARQL language is strictly more expressive
than property paths and nested expressions. The additional expressivity can be
used for modelling graph similarities, graph summarization and ontology
alignment. Despite the increasing expressivity, we show that cfSPARQL still
enjoys a low computational complexity and can be evaluated efficiently.Comment: 25 page
Similarity and bisimilarity notions appropriate for characterizing indistinguishability in fragments of the calculus of relations
Motivated by applications in databases, this paper considers various
fragments of the calculus of binary relations. The fragments are obtained by
leaving out, or keeping in, some of the standard operators, along with some
derived operators such as set difference, projection, coprojection, and
residuation. For each considered fragment, a characterization is obtained for
when two given binary relational structures are indistinguishable by
expressions in that fragment. The characterizations are based on appropriately
adapted notions of simulation and bisimulation.Comment: 36 pages, Journal of Logic and Computation 201
Regular Queries on Graph Databases
Graph databases are currently one of the most popular paradigms for storing data. One of the key conceptual differences between graph and relational databases is the focus on navigational queries that ask whether some nodes are connected by paths satisfying certain restrictions. This focus has driven the definition of several different query languages and the subsequent study of their fundamental properties.
We define the graph query language of Regular Queries, which is a natural extension of unions of conjunctive 2-way regular path queries (UC2RPQs) and unions of conjunctive nested 2-way regular path queries (UCN2RPQs). Regular queries allow expressing complex regular patterns between nodes. We formalize regular queries as nonrecursive Datalog programs with transitive closure rules. This language has been previously considered, but its algorithmic properties are not well understood.
Our main contribution is to show elementary tight bounds for the containment problem for regular queries. Specifically, we show that this problem is 2EXPSPACE-complete. For all extensions of regular queries known to date, the containment problem turns out to be non-elementary. Together with the fact that evaluating regular queries is not harder than evaluating UCN2RPQs, our results show that regular queries achieve a good balance between expressiveness and complexity, and constitute a well-behaved class that deserves further investigation
Structural characterizations of the navigational expressiveness of relation algebras on a tree
Given a document D in the form of an unordered node-labeled tree, we study
the expressiveness on D of various basic fragments of XPath, the core
navigational language on XML documents. Working from the perspective of these
languages as fragments of Tarski's relation algebra, we give characterizations,
in terms of the structure of D, for when a binary relation on its nodes is
definable by an expression in these algebras. Since each pair of nodes in such
a relation represents a unique path in D, our results therefore capture the
sets of paths in D definable in each of the fragments. We refer to this
perspective on language semantics as the "global view." In contrast with this
global view, there is also a "local view" where one is interested in the nodes
to which one can navigate starting from a particular node in the document. In
this view, we characterize when a set of nodes in D can be defined as the
result of applying an expression to a given node of D. All these definability
results, both in the global and the local view, are obtained by using a robust
two-step methodology, which consists of first characterizing when two nodes
cannot be distinguished by an expression in the respective fragments of XPath,
and then bootstrapping these characterizations to the desired results.Comment: 58 Page