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For many problems arising in the setting of graph querying (such as finding semantic associations in RDF graphs, exact and approximate pattern matching, sequence alignment, etc.), the power of standard languages such as the widely studied conjunctive regular path queries (CRPQs) is insufficient in at least two ways. First, they cannot output paths and second, more crucially, they cannot express relations among paths.We thus propose a class of extended CRPQs, called ECRPQs, which add regular relations on tuples of paths, and allow path variables in the heads of queries. We provide several examples of their usefulness in querying graph structured data, and study their properties. We analyze query evaluation and representation of tuples of paths in the output by means of automata. We present a detailed analysis of data and combined complexity of queries, and consider restrictions that lower the complexity of ECRPQs to that of relational conjunctive queries. We study the containment problem, and look at further extensions with first-order features, and with non-regular relations that express arithmetic properties of paths, based on the lengths and numbers of occurrences of labels.

Data exchange is the problem of finding an instance of a target schema, given an instance of a source schema and a specification of the relationship between the source and the target, and answering queries over target instances in a way that is semantically consistent with the information in the source. Theoretical foundations of data exchange have been actively explored recently. It was also noticed that the standard certain answers semantics may behave in very odd ways.In this paper I explain that this behavior is due to the fact that the presence of incomplete information in target instances has been ignored; in particular, proper query evaluation techniques for databases with nulls have not been used, and the distinction between closed and open world semantics has not been made. I present a concept of target solutions based on the closed world assumption, and show that the space of all solutions has two extreme points: the canonical universal solution and the core, well studied in data exchange. I show how to define semantics of query answering taking into account incomplete information, and show that the well-known anomalies go away with the new semantics. The paper also contains results on the complexity of query answering, upper approximations to queries (maybe-answers), and various extensions.

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The article investigates XML document specifications with DTDs and integrity constraints, such as keys and foreign keys. We study the consistency problem of checking whether a given specification is meaningful: that is, whether there exists an XML document that both conforms to the DTD and satisfies the constraints. We show that DTDs interact with constraints in a highly intricate way and as a result, the consistency problem in general is undecidable. When it comes to unary keys and foreign keys, the consistency problem is shown to be NP-complete. This is done by coding DTDs and integrity constraints with linear constraints on the integers. We consider the variations of the problem (by both restricting and enlarging the class of constraints), and identify a number of tractable cases, as well as a number of additional NP-complete ones. By incorporating negations of constraints, we establish complexity bounds on the implication problem, which is shown to be coNP-complete for unary keys and foreign keys.

The expressive power of first-order query languages with several classes of equality and inequality constraints is studied in this paper. We settle the conjecture that recursive queries such as parity test and transitive closure cannot be expressed in the relational calculus augmented with polynomial inequality constraints over the reals. Furthermore, noting that relational queries exhibit several forms of genericity, we establish a number of collapse results of the following form: The class of generic Boolean queries expressible in the relational calculus augmented with a given class of constraints coincides with the class of queries expressible in the relational calculus (with or without an order relation). We prove such results for both the natural and active-domain semantics. As a consequence, the relational calculus augmented with polynomial inequalities expresses the same classes of generic Boolean queries under both the natural and active-domain semantics.In the course of proving these results for the active-domain semantics, we establish Ramsey-type theorems saying that any query involving certain kinds of constraints coincides with a constraint-free query on databases whose elements come from a certain infinite subset of the domain. To prove the collapse results for the natural semantics, we make use of techniques from nonstandard analysis and from the model theory of ordered structures.

We study the problem of efficient maintenance of materi-

Graph data models received much attention lately due to applications in social networks, semantic web, biological databases and other areas. Typical query languages for graph databases retrieve their topology, while actual data stored in them is usually queried using standard relational mechanisms.Our goal is to develop techniques that combine these two modes of querying, and give us query languages that can ask questions about both data and topology. As the basic querying mechanism we consider regular path queries, with the key difference that conditions on paths between nodes now talk not only about labels but also specify how data changes along the path. Paths that combine edge labels with data values are closely related to data words, so for stating conditions in queries, we look at several data-word formalisms developed recently. We show that many of them immediately lead to intractable data complexity for graph queries, with the notable exception of register automata, which can specify many properties of interest, and have NLOGSPACE data and PSPACE combined complexity. As register automata themselves are not easy to use in querying, we define two types of extensions of regular expressions that are more userfriendly, and develop query evaluation techniques for them. For one class, regular expressions with memory, we achieve the same bounds as for automata, and for the other class, regular expressions with equality, we also obtain tractable combined complexity of query evaluation. In addition, we show that results extends to analogs of conjunctive regular path queries.