On IO-Copying and Mildly-Context Sensitive Formalisms

International audienceThe class of mildly context-sensitive languages is commonly regarded as sufficiently rich to capture most aspects of the syntax of natural languages. Many formalisms are known to generate families of languages which belong to this class. Among them are tree-adjoining grammars, multiple context-free grammars and abstract categorial grammars. All these formalisms have in common that they are based on operations which do not copy already derived material in the course of a derivation. We propose an extension of the class of languages captured by these formalisms that is arguably mildly context-sensitive. This extension is based on a mild use of a copying operation we call IO-substitution

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