Linear context-free rewriting systems and deterministic tree-walking transducers

We show that the class of string languages generated by linear context-free rewriting systems is equal to the class of output languages of deterministic tree- walking transducers. From equivalences that have previously been established we know that this class of languages is also equal to the string languages generated by context-free hypergraph grammars, multicomponent tree-adjoining grammars, and multiple contextfree grammars and to the class of yields of images of the regular tree languages under finite-copying top- down tree transducers

Multiple Context-Free Tree Grammars: Lexicalization and Characterization

Multiple (simple) context-free tree grammars are investigated, where "simple" means "linear and nondeleting". Every multiple context-free tree grammar that is finitely ambiguous can be lexicalized; i.e., it can be transformed into an equivalent one (generating the same tree language) in which each rule of the grammar contains a lexical symbol. Due to this transformation, the rank of the nonterminals increases at most by 1, and the multiplicity (or fan-out) of the grammar increases at most by the maximal rank of the lexical symbols; in particular, the multiplicity does not increase when all lexical symbols have rank 0. Multiple context-free tree grammars have the same tree generating power as multi-component tree adjoining grammars (provided the latter can use a root-marker). Moreover, every multi-component tree adjoining grammar that is finitely ambiguous can be lexicalized. Multiple context-free tree grammars have the same string generating power as multiple context-free (string) grammars and polynomial time parsing algorithms. A tree language can be generated by a multiple context-free tree grammar if and only if it is the image of a regular tree language under a deterministic finite-copying macro tree transducer. Multiple context-free tree grammars can be used as a synchronous translation device.Comment: 78 pages, 13 figure

Two characterisation results of multiple context-free grammars and their application to parsing

In the first part of this thesis, a Chomsky-Schützenberger characterisation and an automaton characterisation of multiple context-free grammars are proved. Furthermore, a framework for approximation of automata with storage is described. The second part develops each of the three theoretical results into a parsing algorithm

Dependency structures and lexicalized grammars

In this dissertation, we show that that both the generative capacity and the parsing complexity of lexicalized grammar formalisms are systematically related to structural properties of the dependency structures that these formalisms can induce. Dependency structures model the syntactic dependencies among the words of a sentence. We identify three empirically relevant classes of dependency structures, and show how they can be characterized both in terms of restrictions on the relation between dependency and word-order and within an algebraic framework. In the second part of the dissertation, we develop natural notions of automata and grammars for dependency structures, show how these yield infinite hierarchies of ever more powerful dependency languages, and classify several grammar formalisms with respect to the languages in these hierarchies that they are able to characterize. Our results provide fundamental insights into the relation between dependency structures and lexicalized grammars.In dieser Arbeit zeigen wir, dass sowohl die Ausdrucksmächtigkeit als auch die Verarbeitungskomplexität von lexikalisierten Grammatikformalismen auf systematische Art und Weise von strukturellen Eigenschaften der Dependenzstrukturen abhängen, die diese Formalismen induzieren. Dependenzstrukturen modellieren die syntaktischen Abhängigkeiten zwischen den Wörtern eines Satzes. Wir identifizieren drei empirisch relevante Klassen von Dependenzstrukturen und zeigen, wie sich diese sowohl durch Einschränkungen der Interaktion zwischen Dependenz und Wortstellung, als auch in einem algebraischen Rahmen charakterisieren lassen. Im zweiten Teil der Arbeit entwickeln wir natürliche Begriffe von Automaten und Grammatiken für Dependenzstrukturen, zeigen, wie diese zu unendlichen Hierarchien immer ausdrucksmächtigerer Dependenzsprachen führen, und klassifizieren mehrere Grammatikformalismen in Bezug auf die Sprachen in diesen Hierarchien, die von ihnen charakterisiert werden können. Unsere Resultate liefern grundlegende Einsichten in das Verhältnis zwischen Dependenzstrukturen und lexikalisierten Grammatiken

Mathematical linguistics

but in fact this is still an early draft, version 0.56, August 1 2001. Please d

Uniform vs. Nonuniform Membership for Mildly Context-Sensitive Languages : A Brief Survey

Parsing for mildly context-sensitive language formalisms is an important area within natural language processing. While the complexity of the parsing problem for some such formalisms is known to be polynomial, this is not the case for all of them. This article presents a series of results regarding the complexity of parsing for linear context-free rewriting systems and deterministic tree-walking transducers. We discuss the difference between uniform and nonuniform complexity measures and how parameterized complexity theory can be used to investigate how different aspects of the formalisms influence how hard the parsing problem is. The main results we survey are all hardness results and indicate that parsing is hard even for relatively small values of parameters such as rank and fan-out in a rewriting system.Parameterized Natural Language Parsin

Uniform vs. Nonuniform Membership for Mildly Context-Sensitive Languages: A Brief Survey

Parsing for mildly context-sensitive language formalisms is an important area within natural language processing. While the complexity of the parsing problem for some such formalisms is known to be polynomial, this is not the case for all of them. This article presents a series of results regarding the complexity of parsing for linear context-free rewriting systems and deterministic tree-walking transducers. We discuss the difference between uniform and nonuniform complexity measures and how parameterized complexity theory can be used to investigate how different aspects of the formalisms influence how hard the parsing problem is. The main results we survey are all hardness results and indicate that parsing is hard even for relatively small values of parameters such as rank and fan-out in a rewriting system

Uniform vs. Nonuniform Membership for Mildly Context-Sensitive Languages: A Brief Survey

Parsing for mildly context-sensitive language formalisms is an important area within natural language processing. While the complexity of the parsing problem for some such formalisms is known to be polynomial, this is not the case for all of them. This article presents a series of results regarding the complexity of parsing for linear context-free rewriting systems and deterministic tree-walking transducers. We discuss the difference between uniform and nonuniform complexity measures and how parameterized complexity theory can be used to investigate how different aspects of the formalisms influence how hard the parsing problem is. The main results we survey are all hardness results and indicate that parsing is hard even for relatively small values of parameters such as rank and fan-out in a rewriting system