Another Facet of LIG Parsing

TL;DR

This paper introduces a new parsing algorithm for linear indexed grammars that constructs a context-free grammar representing valid derivations for a given string, with potential practical efficiency improvements.

Contribution

The paper presents a novel parsing method for LIGs that constructs a context-free grammar of derivations, with an ${ m O}(n^6)$ worst-case complexity and improved average-case performance.

Findings

Constructs a context-free grammar of derivations for LIGs

Parsing can be done in linear time relative to parse tree size

Average case performance is significantly better than worst-case

Abstract

In this paper we present a new parsing algorithm for linear indexed grammars (LIGs) in the same spirit as the one described in (Vijay-Shanker and Weir, 1993) for tree adjoining grammars. For a LIG $L$ and an input string $x$ of length $n$, we build a non ambiguous context-free grammar whose sentences are all (and exclusively) valid derivation sequences in $L$ which lead to $x$. We show that this grammar can be built in ${\cal O}(n^6)$ time and that individual parses can be extracted in linear time with the size of the extracted parse tree. Though this ${\cal O}(n^6)$ upper bound does not improve over previous results, the average case behaves much better. Moreover, practical parsing times can be decreased by some statically performed computations.