Matthias Niewerth

Schema design for XML repositories: complexity and tractability

Abiteboul et al. initiated the systematic study of distributed XML documents consisting of several logical parts, possibly located on different machines. The physical distribution of such documents immediately raises the following question: how can a global schema for the distributed document be broken up into local schemas for the different logical parts? The desired set of local schemas should guarantee that, if each logical part satisfies its local schema, then the distributed document satisfies the global schema. Abiteboul et al. proposed three levels of desirability for local schemas: local typing, maximal local typing, and perfect local typing. Immediate algorithmic questions are: (i) given a typing, determine whether it is local, maximal local, or perfect, and (ii) given a document and a schema, establish whether a (maximal) local or perfect typing exists. This paper improves the open complexity results in their work and initiates the study of (i) and (ii) for schema restrictions arising from the current standards: DTDs and XML Schemas with deterministic content models. The most striking result is that these restrictions yield tractable complexities for the perfect typing problem. Furthermore, an open problem in Formal Language Theory is settled: deciding language primality for deterministic finite automata is pspace-complete.

Descriptional complexity of deterministic regular expressions

We study the descriptional complexity of regular languages that are definable by deterministic regular expressions. First, we examine possible blow-ups when translating between regular expressions, deterministic regular expressions, and deterministic automata. Then we give an overview of the closure properties of these languages under various language-theoretic operations and we study the descriptional complexity of applying these operations. Our main technical result is a general property that implies that the blow-up when translating a DFA to an equivalent deterministic expression can be exponential.

BonXai: Combining the simplicity of DTD with the expressiveness of XML Schema

While the migration from DTD to XML Schema was driven by a need for increased expressivity and flexibility, the latter was also significantly more complex to use and understand. Whereas DTDs are characterized by their simplicity, XML Schema Definitions (XSDs) are notoriously difficult. In this paper, we introduce the XML specification language BonXai which possesses most features of XSDs, including its expressivity, while retaining the simplicity of DTDs. In brief, the latter is achieved by sacrificing the explicit use of types in favor of simple patterns expressing contexts for elements. The goal of BonXai is by no means to replace XML Schema, but rather to provide a simpler DTD-like alternative to schema designers that do not need the explicit use of types. Therefore, BonXai can be seen as a practical front-end for XML Schema. A particular strong point of BonXai is its solid foundation rooted in a decade of theoretical work around pattern-based schemas. We present in detail the formal model for BonXai and discuss translation algorithms to and from XML Schema.

Two-variable logic and key constraints on data words

The paper introduces key constraints for data words and shows that it is decidable whether, for a given two-variable sentence ϕ that can refer to the successor relation on positions and a set Κ of key constraints, there is a data string w that satisfies ϕ and respects Κ. Here, the formula is allowed to refer to the successor relation but not to the linear order on the positions of the word. As a byproduct, a self-contained exposition of an algorithm that decides satisfiability of such formulas (without key constraints) in 2-nexptime is given.

On the state complexity of closures and interiors of regular languages with subwords and superwords

The downward and upward closures of a regular language L are obtained by collecting all the subwords and superwords of its elements, respectively. The downward and upward interiors of L are obtained dually by collecting words having all their subwords and superwords in L, respectively. We provide lower and upper bounds on the size of the smallest automata recognizing these closures and interiors. We also consider the computational complexity of decision problems for closures of regular languages.

Developing and analyzing XSDs through BonXai

BonXai is a versatile schema specification language expressively equivalent to XML Schema. It is not intended as a replacement for XML Schema but it can serve as an additional, user-friendly front-end. It offers a simple way and a lightweight syntax to specify the context of elements based on regular expressions rather than on types. In this demo we show the front-end capabilities of BonXai and exemplify its potential to offer a novel way to view existing XML Schema Definitions. In particular, we present several usage scenarios specifically targeted to showcase the ease of specifying, modifying, and understanding XML Schema Definitions through BonXai.

Minimization of Tree Pattern Queries

We investigate minimization of tree pattern queries that use the child relation, descendant relation, node labels, and wildcards. We prove that minimization for such tree patterns is Sigma2P-complete and thus solve a problem first attacked by Flesca, Furfaro, and Masciari in 2003. We first provide an example that shows that tree patterns cannot be minimized by deleting nodes. This example shows that the M-NR conjecture, which states that minimality of tree patterns is equivalent to their nonredundancy, is false. We then show how the example can be turned into a gadget that allows us to prove Sigma2P-completeness.

Definability by Weakly Deterministic Regular Expressions with Counters is Decidable

We show that weakly deterministic regular expressions with counters (WDREs) —as they are used in XML Schema— are at most exponentially larger than equivalent DFAs. As a consequence, the problem, whether a given DFA is equivalent to any WDRE, is decidable in EXPSPACE.

Enumeration of MSO Queries on Strings with Constant Delay and Logarithmic Updates

We consider the enumeration of MSO queries over strings under updates. For each MSO query we build an index structure enjoying the following properties: The index structure can be constructed in linear time, it can be updated in logarithmic time and it allows for constant delay time enumeration. This improves from the previous known index structures allowing for constant delay enumeration that would need to be reconstructed from scratch, hence in linear time, in the presence of updates. We allow relabeling updates, insertion of individual labels and removal of individual labels.

Reasoning About XML Constraints Based on XML-to-Relational Mappings

The article introduces a simple framework for the specification of constraints for XML documents in which constraints are specified by (1) a mapping that extracts a relation from every XML document and (2) a relational constraint on the resulting relation. The mapping has to be generic with respect to the actual data values and the relational constraints can be of any kind. Besides giving a general undecidability result for first-order definable mappings and a general decidability result for MSO definable mappings for restricted functional dependencies, the article studies the complexity of the implication problem for XML constraints that are specified by tree pattern queries and functional dependencies. Furthermore, it highlights how other specification languages for XML constraints can be formulated in the framework.