11 research outputs found
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
Axiomatizations for downward XPath on Data Trees
We give sound and complete axiomatizations for XPath with data tests by
"equality" or "inequality", and containing the single "child" axis. This
data-aware logic predicts over data trees, which are tree-like structures whose
every node contains a label from a finite alphabet and a data value from an
infinite domain. The language allows us to compare data values of two nodes but
cannot access the data values themselves (i.e. there is no comparison by
constants). Our axioms are in the style of equational logic, extending the
axiomatization of data-oblivious XPath, by B. ten Cate, T. Litak and M. Marx.
We axiomatize the full logic with tests by "equality" and "inequality", and
also a simpler fragment with "equality" tests only. Our axiomatizations apply
both to node expressions and path expressions. The proof of completeness relies
on a novel normal form theorem for XPath with data tests
Axiomatizing hybrid xpath with data
In this paper we introduce sound and strongly complete axiomatizations for XPath with data constraints extended with hybrid operators. First, we present HXPath=, a multi-modal version of XPath with data, extended with nominals and the hybrid operator @. Then, we introduce an axiomatic system for HXPath=, and we prove it is strongly complete with respect to the class of abstract data models, i.e., data models in which data values are abstracted as equivalence relations. We prove a general completeness result similar to the one presented in, e.g., [BtC06], that ensures that certain extensions of the axiomatic system we introduce are also complete. The axiomatic systems that can be obtained in this way cover a large family of hybrid XPath languages over different classes of frames, for which we present concrete examples. In addition, we investigate axiomatizations over the class of tree models, structures widely used in practice. We show that a strongly complete, finitary, first-order axiomatization of hybrid XPath over trees does not exist, and we propose two alternatives to deal with this issue. We finally introduce filtrations to investigate the status of decidability of the satisfiability problem for these languages.Fil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Fervari, Raul Alberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentin
Axiomatizing Hybrid XPath with Data
In this paper we introduce sound and strongly complete axiomatizations for
XPath with data constraints extended with hybrid operators. First, we present
HXPath=, a multi-modal version of XPath with data, extended with nominals and
the hybrid operator @. Then, we introduce an axiomatic system for HXPath=, and
we prove it is strongly complete with respect to the class of abstract data
models, i.e., data models in which data values are abstracted as equivalence
relations. We prove a general completeness result similar to the one presented
in, e.g., [BtC06], that ensures that certain extensions of the axiomatic system
we introduce are also complete. The axiomatic systems that can be obtained in
this way cover a large family of hybrid XPath languages over different classes
of frames, for which we present concrete examples. In addition, we investigate
axiomatizations over the class of tree models, structures widely used in
practice. We show that a strongly complete, finitary, first-order
axiomatization of hybrid XPath over trees does not exist, and we propose two
alternatives to deal with this issue. We finally introduce filtrations to
investigate the status of decidability of the satisfiability problem for these
languages
CSS Minification via Constraint Solving
Minification is a widely-accepted technique which aims at reducing the size
of the code transmitted over the web. We study the problem of minifying
Cascading Style Sheets (CSS) --- the de facto language for styling web
documents. Traditionally, CSS minifiers focus on simple syntactic
transformations (e.g. shortening colour names). In this paper, we propose a new
minification method based on merging similar rules in a CSS file.
We consider safe transformations of CSS files, which preserve the semantics
of the CSS file. The semantics of CSS files are sensitive to the ordering of
rules in the file. To automatically identify a rule merging opportunity that
best minimises file size, we reduce the rule-merging problem to a problem on
CSS-graphs, i.e., node-weighted bipartite graphs with a dependency ordering on
the edges, where weights capture the number of characters (e.g. in a selector
or in a property declaration). Roughly speaking, the corresponding CSS-graph
problem concerns minimising the total weight of a sequence of bicliques
(complete bipartite subgraphs) that covers the CSS-graph and respects the edge
order.
We provide the first full formalisation of CSS3 selectors and reduce
dependency detection to satisfiability of quantifier-free integer linear
arithmetic, for which highly-optimised SMT-solvers are available. To solve the
above NP-hard graph optimisation problem, we show how Max-SAT solvers can be
effectively employed. We have implemented our algorithms using Max-SAT and
SMT-solvers as backends, and tested against approximately 70 real-world
examples (including the top 20 most popular websites). In our benchmarks, our
tool yields larger savings than six well-known minifiers (which do not perform
rule-merging, but support many other optimisations). Our experiments also
suggest that better savings can be achieved in combination with one of these
six minifiers
Complete axiomatizations for XPath fragments
We provide complete axiomatizations for several fragments of XPath: sets of equivalences from which every other valid equivalence is derivable. Specically, we axiomatize downward single axis fragments of Core XPath (that is, Core XPath(↓) and Core XPath(↓+)) as well as the full Core XPath. We make use of techniques from modal logic
Complete axiomatizations for XPath fragments
We provide complete axiomatizations for several fragments of Core XPath, the navigational core of XPath 10 introduced by Gottlob. Koch and Pichler A complete axiomatization for a given fragment is a set of equivalences from which every other valid equivalence is derivable; equivalences can be thought of as (undirected) rewrite rules. Specifically, we axiomatize single axis fragments of Core XPath as well as full Core XPath Our completeness proofs use results and techniques from modal logic