Alternating register automata on finite words and trees

We study alternating register automata on data words and data trees in relation to logics. A data word (resp. data tree) is a word (resp. tree) whose every position carries a label from a finite alphabet and a data value from an infinite domain. We investigate one-way automata with alternating control over data words or trees, with one register for storing data and comparing them for equality. This is a continuation of the study started by Demri, Lazic and Jurdzinski. From the standpoint of register automata models, this work aims at two objectives: (1) simplifying the existent decidability proofs for the emptiness problem for alternating register automata; and (2) exhibiting decidable extensions for these models. From the logical perspective, we show that (a) in the case of data words, satisfiability of LTL with one register and quantification over data values is decidable; and (b) the satisfiability problem for the so-called forward fragment of XPath on XML documents is decidable, even in the presence of DTDs and even of key constraints. The decidability is obtained through a reduction to the automata model introduced. This fragment contains the child, descendant, next-sibling and following-sibling axes, as well as data equality and inequality tests

XPath satisfiability in the presence of DTDs

We study the satisfiability problem associated with XPath in the presence of DTDs. This is the problem of determining, given a query p in an XPath fragment and a DTD D, whether or not there exists an XML document T such that T conforms to D and the answer of p on T is nonempty. We consider a variety of XPath fragments widely used in practice, and investigate the impact of different XPath operators on the satisfiability analysis. We first study the problem for negation-free XPath fragments with and without upward axes, recursion and data-value joins, identifying which factors lead to tractability and which to NP-completeness. We then turn to fragments with negation but without data values, establishing lower and upper bounds in the absence and in the presence of upward modalities and recursion. We show that with negation the complexity ranges from PSPACE to EXPTIME. Moreover, when both data values and negation are in place, we find that the complexity ranges from NEXPTIME to undecidable. Furthermore, we give a finer analysis of the problem for particular classes of DTDs, exploring the impact of various DTD constructs, identifying tractable cases, as well as providing the complexity in the query size alone. Finally, we investigate the problem for XPath fragments with sibling axes, exploring the impact of horizontal modalities on the satisfiability analysis. © 2008 ACM

Frontiers of tractability for typechecking simple XML transformations

AbstractTypechecking consists of statically verifying whether the output of an XML transformation is always conform to an output type for documents satisfying a given input type. We focus on complete algorithms which always produce the correct answer. We consider top–down XML transformations incorporating XPath expressions and abstract document types by grammars and tree automata. By restricting schema languages and transformations, we identify several practical settings for which typechecking can be done in polynomial time. Moreover, the resulting framework provides a rather complete picture as we show that most scenarios cannot be enlarged without rendering the typechecking problem intractable. So, the present research sheds light on when to use fast complete algorithms and when to reside to sound but incomplete ones

Satisfiability of Downward XPath with Data Equality Tests

International audienceIn this work we investigate the satisfiability problem for the logic XPath(↓*, ↓, =), that includes all downward axes as well as equality and inequality tests. We address this problem in the absence of DTDs and the sibling axis. We prove that this fragment is decidable, and we nail down its complexity, showing the problem to be ExpTime-complete. The result also holds when path expressions allow closure under the Kleene star operator. To obtain these results, we introduce a new automaton model over data trees that captures XPath(↓*, ↓, =) and has an ExpTime emptiness problem. Furthermore, we give the exact complexity of several downward-looking fragments

Mu-Calculus Based Resolution of XPath Decision Problems

XPath is the standard declarative notation for navigating XML data and returning a set of matching nodes. In the context of XSLT/XQuery analysis, query optimization, and XML type checking, XPath decision problems arise naturally. They notably include XPath containment (whether or not for any tree the result of a particular query is included in the result of a second one), and XPath satisfiability (whether or not an expression yields a non-empty result), in the presence (or the absence) of XML DTDs. In this paper, we propose a unifying logic for XML, namely the alternation-free modal mu-calculus with converse. We show how to translate major XML concepts such as XPath and DTDs into this logic. Based on these embeddings, we show how XPath decision problems can be solved using a state-of-the-art EXPTIME decision procedure for mu-calculus satisfiability. We provide preliminary experiments which shed light, for the first time, on the cost of solving XPath decision problems in practice

Processing techniques for partial tree-pattern queries on XML data

In recent years, eXtensible Markup Language (XML) has become a de facto standard for exporting and exchanging data on the Web. XML structures data as trees. Querying capabilities are provided through patterns matched against the XML trees. Research on the processing of XML queries has focused mainly on tree-pattern queries. Tree-pattern queries are not appropriate for querying XML data sources whose structure is not fully known to the user, or for querying multiple data sources which structure information differently. Recently, a class of queries, called Partial Tree-Pattern Queries (PTPQs) was identified. A central feature of PTPQs is that the structure can be specified fully, partially, or not at all in a query. For this reason. PTPQs can be used for flexibly querying XML data sources. This thesis deals with processing techniques for PTPQs. In particular, it addresses the satisfiability, containment and minimization problems for PTPQs. In order to cope with structural expression derivation issues and to compare PTPQs, a set of inference rules is suggested and a canonical form for PTPQs that comprises all derived structural expressions is defined. This canonical form is used for determining necessary and sufficient conditions for PTPQ satisfiability. The containment problem is studied both in the absence and in the presence of structural summaries of data called dimension graphs. It is shown that this problem cannot be characterized by homomorphisms between PTPQs, even when PTPQs are put in canonical form. In both cases of the problem, necessary and sufficient conditions for PTPQ containment are provided in terms of homomorphisms between PTPQs and (a possibly exponential number of) tree-pattern queries. This result is used to identify a subclass of PTPQs that strictly contains tree-pattern queries for which the containment problem can be fully characterized through the existence of homomorphisms. To cope with the high complexity of PTPQ containment, heuristic approaches for this problem are designed that trade accuracy for speed. The heuristic approaches equivalently add structural expressions to PTPQs in order to increase the possibility for a homomorphism between two contained PTPQs to exist. An implementation and extensive experimental evaluation of these heuristics shows that they are useful in practice, and that they can be efficiently implemented in a query optimizer. The goal of PTPQ minimization is to produce an equivalent PTPQ which is syntactically smaller in size. This problem is studied in the absence of structural summaries. It is shown that PTPQs cannot be minimized by removing redundant parts as is the case with certain classes of tree-pattern queries. It is also shown that, in general, a PTPQ does not have a unique minimal equivalent PTPQ. Finally, sound, but not complete, heuristic approaches for PTPQ minimization are presented. These approaches gradually trade execution time for accuracy

Reasoning About Pattern-Based XML Queries

Abstract. We survey results about static analysis of pattern-based 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 pattern-based queries in reasoning about schema mappings for data exchange.