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

Model Checking Parse Trees

Parse trees are fundamental syntactic structures in both computational linguistics and compilers construction. We argue in this paper that, in both fields, there are good incentives for model-checking sets of parse trees for some word according to a context-free grammar. We put forward the adequacy of propositional dynamic logic (PDL) on trees in these applications, and study as a sanity check the complexity of the corresponding model-checking problem: although complete for exponential time in the general case, we find natural restrictions on grammars for our applications and establish complexities ranging from nondeterministic polynomial time to polynomial space in the relevant cases.Comment: 21 + x page

Two-Variable Logic on Data Trees and XML Reasoning

International audienceMotivated by reasoning tasks in the context of XML languages, the satisfiability problem of logics on data trees is investigated. The nodes of a data tree have a label from a finite set and a data value from a possibly infinite set. It is shown that satisfiability for two-variable first-order logic is decidable if the tree structure can be accessed only through the child and the next sibling predicates and the access to data values is restricted to equality tests. From this main result decidability of satisfiability and containment for a data-aware fragment of XPath and of the implication problem for unary key and inclusion constraints is concluded

Ensuring Query Compatibility with Evolving XML Schemas

During the life cycle of an XML application, both schemas and queries may change from one version to another. Schema evolutions may affect query results and potentially the validity of produced data. Nowadays, a challenge is to assess and accommodate the impact of theses changes in rapidly evolving XML applications. This article proposes a logical framework and tool for verifying forward/backward compatibility issues involving schemas and queries. First, it allows analyzing relations between schemas. Second, it allows XML designers to identify queries that must be reformulated in order to produce the expected results across successive schema versions. Third, it allows examining more precisely the impact of schema changes over queries, therefore facilitating their reformulation

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

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

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

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