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

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

A Sequent Calculus for a Modal Logic on Finite Data Trees

We investigate the proof theory of a modal fragment of XPath equipped with data (in)equality tests over finite data trees, i.e., over finite unranked trees where nodes are labelled with both a symbol from a finite alphabet and a single data value from an infinite domain. We present a sound and complete sequent calculus for this logic, which yields the optimal PSPACE complexity bound for its validity problem

Algoritmos de tableaux para Xpath con datos

En este trabajo se presenta un cálculo correcto y completo para XPath con datos y caminos descendentes, enriquecido con nominales y operadores de satisfacción. Llamaremos HXPath = (↓) al lenguaje híbrido que resulta de agregar operadores híbridos a XPath. Primero se mencionan aspectos básicos de las lógicas modales, híbridas y de XPath, para luego dar el cálculo de tableaux para XPath = . Finalmente se demuestra completitud del cálculo.En este trabajo se desarrollaron complementos para el sistema de información geográfica QGIS que permiten el preprocesamiento y análisis de series de tiempo del Índice de Vegetación Normalizado (NDVI), útiles para estudiar y comparar la estructura vegetal de diferentes puntos geográficos de interés, a través del tiempo. Las series fueron extraídas a partir de imágenes obtenidas por el sensor MODIS (Moderate Resolution Imaging Spectroradiometer), por un biólogo especialista.Fil: Seiler, Nahuel Germán. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina

Transitive closure logic, nested tree walking automata, and XPath

International audienceWe study FO(MTC), first-order logic with monadic transitive closure, a logical formalism in between FO and MSO on trees. We characterize the expressive power of FO(MTC) in terms of nested tree-walking automata. Using the latter, we show that FO(MTC) is strictly less expressive than MSO, solving an open problem. We also present a temporal logic on trees that is expressively complete for FO(MTC), in the form of an extension of the XML document navigation language XPath with two operators: the Kleene star for taking the transitive closure of path expressions, and a subtree relativisation operator, allowing one to restrict attention to a specific subtree while evaluating a subexpression. We show that the expressive power of this XPath dialect equals that of FO(MTC) for Boolean, unary and binary queries. We also investigate the complexity of the automata model as well as the XPath dialect. We show that query evaluation be done in polynomial time (combined complexity), but that emptiness (or, satisfiability) is 2ExpTime-complete

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