Multiple Context-Free Tree Grammars: Lexicalization and Characterization

TL;DR

This paper explores multiple context-free tree grammars, demonstrating their lexicalization, equivalence to other grammar formalisms, and their computational properties, including parsing complexity and translation capabilities.

Contribution

It introduces lexicalization techniques for finitely ambiguous grammars and characterizes their generative power and relation to other formal systems.

Findings

Finitely ambiguous grammars can be lexicalized with minimal increase in rank and fan-out.

Multiple context-free tree grammars have the same power as multi-component tree adjoining grammars.

They can generate exactly the images of regular tree languages under deterministic macro tree transducers.

Abstract

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.