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Reasoning About PatternBased XML Queries
"... We survey results about static analysis of patternbased queries over XML documents. These queries are analogs of conjunctive queries, their unions and Boolean combinations, in which tree patterns play the role of atomic formulae. As in the relational case, they can be viewed as both queries and in ..."
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We survey results about static analysis of patternbased queries over XML documents. These queries are analogs of conjunctive queries, their unions and Boolean combinations, in which tree patterns play the role of atomic formulae. As in the relational case, they can be viewed as both queries and incomplete documents, and thus static analysis problems can also be viewed as finding certain answers of queries over such documents. We look at satisfiability of patterns under schemas, containment of queries for various features of XML used in queries, finding certain answers, and applications of patternbased queries in reasoning about schema mappings for data exchange.
How Big Must Complete XML Query Languages Be?
"... Marx and de Rijke have shown that the navigational core of the w3c XML query language XPath is not firstorder complete – that is it cannot express every query definable in firstorder logic over the navigational predicates. How can one extend XPath to get a firstorder complete language? Marx has sh ..."
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Marx and de Rijke have shown that the navigational core of the w3c XML query language XPath is not firstorder complete – that is it cannot express every query definable in firstorder logic over the navigational predicates. How can one extend XPath to get a firstorder complete language? Marx has shown that Conditional XPath – an extension of XPath with an “Until ” operator – is first order complete. The completeness argument makes essential use of the presence of upward axes in Conditional XPath. We examine whether it is possible to get “forwardonly ” languages that are firstorder complete for XML Boolean queries. It is easy to see that a variant of the temporal logic CTL ∗ is firstorder complete; the variant has path quantifiers for downward, leftward and rightward paths, while along a path one can check arbitrary formulas of linear temporal logic (LTL). This language has two major disadvantages: it requires path quantification in both horizontal directions (in particular, it requires looking backward at the prior siblings of a node), and it requires the consideration of formulas of LTL of arbitrary complexity on vertical paths. This last is in contrast with Marx’s Conditional XPath, which requires only the checking of a single Until operator on a path. We investigate whether either of these restrictions can be eliminated. Our main results are negative ones. We show that if we restrict our CTL ∗ language by having an until operator in only one horizontal direction, then we lose completeness. We also show that no restriction to a “small ” subset of LTL along vertical paths is sufficient for first order completeness. Smallness here means of bounded “Until Depth”, a measure of complexity of LTL formulas defined by Etessami and Wilke. In particular, it follows from our work that Conditional XPath with only forward axes is not expressively complete; this extends results proved by Rabinovich and Maoz in the context of infinite unordered trees.
Static Analysis of XML Security Views and Query Rewriting
 INFORMATION AND COMPUTATION
, 2013
"... In this paper, we revisit the view based security framework for XML without imposing any of the previously considered restrictions on the class of queries, the class of DTDs, and the type of annotations used to define the view. First, we study query rewriting with views when the classes used to defi ..."
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In this paper, we revisit the view based security framework for XML without imposing any of the previously considered restrictions on the class of queries, the class of DTDs, and the type of annotations used to define the view. First, we study query rewriting with views when the classes used to defined queries and views are Regular XPath and MSO. Next, we investigate problems of static analysis of security access specifications (SAS): we introduce the novel class of intervalbounded SAS and we define three different manners to compare views (i.e. on queries), with a security point of view. We provide a systematic study of the complexity for deciding these three comparisons, when the depth of the XML documents is bounded, when the document may have an arbitrary depth but the queries defining the views are restricted to guarantee the intervalbounded property, and in the general setting without restriction on queries and document.
Representing and Querying Incomplete Information: a Data Interoperability Perspective
, 2014
"... This thesis is intended to be a succinct and rather informal presentation of some of my most recent work, which has been done in collaboration with several other people. In particular this thesis concentrates on our contributions to the study of incomplete information in the context of data interope ..."
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This thesis is intended to be a succinct and rather informal presentation of some of my most recent work, which has been done in collaboration with several other people. In particular this thesis concentrates on our contributions to the study of incomplete information in the context of data interoperability. In this scenario data is heterogenous and decentralized, needs to be integrated from several sources and exchanged between different applications. Incompleteness, i.e. the presence of “missing” or “unknown” portions of data, is naturally generated in data exchange and integration, due to data heterogeneity. The management of incomplete information poses new challenges in this context. The focus of our study is the development of models of incomplete information suitable to data interoperability tasks, and the study of techniques for efficiently querying several forms of incompleteness. The work presented in Chapter 4 is ongoing in the context of Nadime Francis’s PhD, whom I am cosupervising together with Luc Segoufin.
ViewBased TreeLanguage Rewritings for XML
"... Abstract. We study query rewriting using views (QRV) for XML. Our queries and views are regular tree languages (RTLs) represented by tree automata over marked alphabets, where the markers serve as "node selectors". We formally define query rewriting using views for RTLs and give an automa ..."
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Abstract. We study query rewriting using views (QRV) for XML. Our queries and views are regular tree languages (RTLs) represented by tree automata over marked alphabets, where the markers serve as "node selectors". We formally define query rewriting using views for RTLs and give an automatabased algorithm to compute the maximally contained rewriting. The formalism we use is equal in power with Monadic Second Order (MSO) logic, and our algorithm for computing QRV is the first to target this expressive class. Furthermore we prove a tight lower bound, thus showing that our algorithm is optimal. Another strength of our automatabased approach is that we are able to cast computing QRV into executing a sequence of intuitive operations on automata, thus rendering our approach practical as it can be easily implemented utilizing offtheshelf automata toolboxes. Finally, we generalize our framework to account for more complex queries in the spirit of the FOR clause in XQuery. For this generalization as well, we give an optimal algorithm for computing the maximally contained rewriting of queries using views.
Validity of Positive XPath Queries with . . .
, 2011
"... This paper discusses the validity problem for positive XPath queries with wildcard in the presence of DTDs. A given XPath query p is valid under a DTD D if, for every XML document T conforming to D, the answer to p on T is nonempty. The validity problem is one of the basic static analyses of queries ..."
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This paper discusses the validity problem for positive XPath queries with wildcard in the presence of DTDs. A given XPath query p is valid under a DTD D if, for every XML document T conforming to D, the answer to p on T is nonempty. The validity problem is one of the basic static analyses of queries, together with the satisfiability and the containment problems. Although the validity problem is the dual of the satisfiability problem, the complexity of validity for positive XPath classes is not obvious because the XPath class does not contain the negation operator. In this paper, first, it is shown that the path union operator in XPath queries easily makes the validity problem intractable. Then, we focus on wildcard, which is a special case of path union and more popular than path union in the real world. Interestingly, wildcard together with child and descendantorself axes and qualifier causes intractability while the validity problem becomes tractable for XPath classes defined by any combination of three of child axis, descendantorself axis, qualifier, and wildcard.
Expressive Logical Combinators for Free
, 2013
"... Abstract. A popular technique in the static analysis for query languages relies on the construction of compilers that effectively translate queries into logical formulas. These formulas are then solved for satisfiability using an offtheshelf satisfiability solver. A critical aspect in this approac ..."
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Abstract. A popular technique in the static analysis for query languages relies on the construction of compilers that effectively translate queries into logical formulas. These formulas are then solved for satisfiability using an offtheshelf satisfiability solver. A critical aspect in this approach is the size of the obtained logical formula, since it constitutes a factor that affects the combined complexity of the global approach. We show that a whole class of logical combinators (or “macros”) can be used as an intermediate language between the query language and the logical language. Those logical combinators provide an exponential gain in succinctness over the corresponding explicit logical representation, yet preserving the typical exponential time complexity of the subsequent logical decision procedure. This opens the way for solving a wide range of problems such as satisfiability and containment for expressive query languages in exponentialtime, even though their direct formulation into the underlying logic results in an exponential blowup of the formula size, yielding an incorrectly presumed twoexponential time complexity. We illustrate this from a very practical point of view on a few examples such as numerical occurrence constraints and tree frontier properties which are concrete problems found in the XML world. 1
Optimized XPath translation to query automata
"... Linear Temporal Logic (LTL) is one of the main tools used extensively in the field of verification, where many efficient modelchecking algorithms have been developed over the years. Recently a tree analog of LTL has been proposed, where a modification of the LTLtoAutomata translation was introduc ..."
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Linear Temporal Logic (LTL) is one of the main tools used extensively in the field of verification, where many efficient modelchecking algorithms have been developed over the years. Recently a tree analog of LTL has been proposed, where a modification of the LTLtoAutomata translation was introduced. This made it possible to use automata techniques for reasoning about properties of XML queries and specifications such as containment of XPath expressions, optimisation of XPath expressions under schema constraints, and security properties of XML views. However, as the size of the constructed automata grows, there is a need for optimisation techniques to reduce the size of constructed automata. The goal of this report is to construct an optimised automaton and to implement the translation from XPath to automata and use it on XML reasoning tasks. i Acknowledgements I would like to thank my supervisor, Professor. Leonid Libkin for introducing me to the world of automata and their connection with database systems. I am also grateful to Tony Tan for his support and guidance throughout the project and for his patience with me!
View update translation for XML
 14TH INTERNATIONAL CONFERENCE ON DATABASE THEORY (ICDT)
, 2011
"... We study the problem of update translation for views on XML documents. More precisely, given an XML view definition and a user defined view update program, find a source update program that translates the view update without side effects on the view. Additionally, we require the translation to be de ..."
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We study the problem of update translation for views on XML documents. More precisely, given an XML view definition and a user defined view update program, find a source update program that translates the view update without side effects on the view. Additionally, we require the translation to be defined on all possible source documents; this corresponds to Hegnerâs notion of uniform translation. The existence of such translation would allow to update XML views without the need of materialization. The class of views we consider can remove parts of the document and rename nodes. Our update programs define the simultaneous application of a collection of atomic update operations among insertion/deletion of a subtree and node renaming. Such update programs are compatible with the XQuery Update Facility (XQUF) snapshot semantics. Both views and update programs are represented by recognizable tree languages. We present as a proof of concept a small fragment of XQUF that can be expressed by our update programs, thus allows for update propagation. Two settings for the update problem are studied: without source constraints, where all source updates are allowed, and with source constraints, where there is a restricted set of authorized source updates. Using tree automata techniques, we establish that without constraints, all view updates are uniformly translatable and the translation is tractable. In presence of constraints, not all view updates are uniformly translatable. However, we introduce a reasonable restriction on update programs for which uniform translation with constraints becomes possible.