The universal generation problem for LFG grammars is the problem of determining whether a given grammar derives any terminal string with a given f-structure. It is known that this problem is decidable for acyclic f-structures. In this brief note, we show that for those f-structures the problem is nonetheless intractable. This holds even for grammars that are off-line parsable.

The formalism for Lexical-Functional Grammar (LFG) was introduced in the 1980s as one of the first constraint-based grammatical formalisms for natural language. It has led to substantial contributions to the linguistic literature and to the construction of large-scale descriptions of particular languages. Investigations of its mathematical properties have shown that, without further restrictions, the recognition, emptiness, and generation problems are undecidable, and that they are intractable in the worst case even with commonly applied restrictions. However, grammars of real languages appear not to invoke the full expressive power of the formalism, as indicated by the fact that algorithms and implementations for recognition and generation have been developed that run—even for broad-coverage grammars—in typically polynomial time. This article formalizes some restrictions on the notation and its interpretation that are compatible with conventions and principles that have been implicit or informally stated in linguistic theory. We show that LFG grammars that respect these restrictions, while still suitable for the description of natural languages, are equivalent to linear context-free rewriting systems and allow for tractable computation.

We present a non-deterministic finite-state transducer that acts as a tokenizer and normalizer for free text that is input to a broad-coverage LFG of German. We compare the basic tokenizer used in an earlier version of the grammar and the more sophisticated tokenizer that we now use. The revised tokenizer increases the coverage of the grammar in terms of full parses from 68.3% to 73.4% on sentences 8,001 through 10,000 of the TiGer Corpus.

February 13-25, 1991