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

Expressing Context-Free Tree Languages by Regular Tree Grammars

In this thesis, three methods are investigated to express context-free tree languages by regular tree grammars. The first method is a characterization. We show restrictions to context-free tree grammars such that, for each restricted context-free tree grammar, a regular tree grammar can be constructed that induces the same tree language. The other two methods are approximations. An arbitrary context-free tree language can be approximated by a regular tree grammar with a restricted pushdown storage. Furthermore, we approximate weighted context-free tree languages, induced by weighted linear nondeleting context-free tree grammars, by showing how to approximate optimal weights for weighted regular tree grammars

New Results on Context-Free Tree Languages

Context-free tree languages play an important role in algebraic semantics and are applied in mathematical linguistics. In this thesis, we present some new results on context-free tree languages