Sebastian Maneth

Tree automata and XPath on compressed trees

The complexity of various membership problems for tree automata on compressed trees is analyzed. Two compressed representations are considered: dags, which allow to share identical subtrees in a tree, and straight-line context-free tree grammars, which moreover allow to share identical intermediate parts of a tree. Several completeness results for the classes NL, P, and PSPACE are obtained. Finally, the complexity of the XPath evaluation problem on trees that are compressed via straight-line context-free tree grammars is investigated.

Efficient memory representation of XML documents

Implementations that load XML documents and give access to them via, e.g., the DOM, suffer from huge memory demands: the space needed to load an XML document is usually many times larger than the size of the document. A considerable amount of memory is needed to store the tree structure of the XML document. Here a technique is presented that allows to represent the tree structure of an XML document in an efficient way. The representation exploits the high regularity in XML documents by “compressing” their tree structure; the latter means to detect and remove repetitions of tree patterns. The functionality of basic tree operations, like traversal along edges, is preserved in the compressed representation. This allows to directly execute queries (and in particular, bulk operations) without prior decompression. For certain tasks like validation against an XML type or checking equality of documents, the representation allows for provably more efficient algorithms than those running on conventional representations.

XML type checking with macro tree transducers

MSO logic on unranked trees has been identified as a convenient theoretical framework for reasoning about expressiveness and implementations of practical XML query languages. As a corresponding theoretical foundation of XML transformation languages, the transformation language TL is proposed. This language is based on the document transformation language DTL of Maneth and Neven which incorporates full MSO pattern matching, arbitrary navigation in the input tree using also MSO patterns, and named procedures. The new language generalizes DTL by additionally allowing procedures to accumulate intermediate results in parameters. It is proved that TL -- and thus in particular DTL - despite their expressiveness still allow for effective inverse type inference. This result is obtained by means of a translation of TL programs into compositions of top-down finite state tree transductions with parameters, also called (stay) macro tree transducers.

A formal model for an expressive fragment of XSLT

The extension of the eXtensible Style sheet Language (XSL) by variables and passing of data values between template rules has generated a powerful XML query language: eXtensible Style sheet Language Transformations (XSLT). An informal introduction to XSTL is given, on the bases of which a formal model of a fragment of XSLT is defined. This formal model is in the spirit of tree transducers, and its semantics is defined by rewrite relations. It is shown that the expressive power of the fragment is already beyond that of most other XML query languages. Finally, important properties such as termination and closure under composition are considered.

Macro Tree Transducers, Attribute Grammars, and MSO Definable Tree Translations

A characterization is given of the class of tree translations definable in monadic second-order logic (MSO), in terms of macro tree transducers. The first main result is that the MSO definable tree translations are exactly those tree translations realized by macro tree transducers (MTTs) with regular look-ahead that are single use restricted. For this the single use restriction known from attribute grammars is generalized to MTTs. Since MTTs are closed under regular look-ahead, this implies that every MSO definable tree translation can be realized by an MTT. The second main result is that the class of MSO definable tree translations can also be obtained by restricting MTTs with regular look-ahead to be finite copying, i.e., to require that each input subtree is processed only a bounded number of times. The single use restriction is a rather strong, static restriction on the rules of an MTT, whereas the finite copying restriction is a more liberal, dynamic restriction on the derivations of an MTT.

A comparison of pebble tree transducers with macro tree transducers

Abstract.The n-pebble tree transducer was recently proposed as a model for XML query languages. The four main results on deterministic transducers are: First, (1) the translation

Exact XML Type Checking in Polynomial Time

tau

A learning algorithm for top-down XML transformations

of an n-pebble tree transducer can be realized by a composition of n+1 0-pebble tree transducers. Next, the pebble tree transducer is compared with the macro tree transducer, a well-known model for syntax-directed semantics, with decidable type checking. The -pebble tree transducer can be simulated by the macro tree transducer, which, by the first result, implies that (2)

Deciding equivalence of top--down XML transformations in polynomial time

tau

Scalable programming abstractions for XML services

can be realized by an (n+1)-fold composition of macro tree transducers. Conversely, every macro tree transducer can be simulated by a composition of 0-pebble tree transducers. Together these simulations prove that (3) the composition closure of n-pebble tree transducers equals that of macro tree transducers (and that of 0-pebble tree transducers). Similar results hold in the nondeterministic case. Finally, (4) the output languages of deterministic n-pebble tree transducers form a hierarchy with respect to the number n of pebbles.