Just-in-time subgrammar extraction for HPSG

We define the basic problem of subgrammar extraction for head-driven phrase structure grammars (HPSG) in the following way: Given a large HPSG grammarG and a set of wordsW , find a small subgrammar of G that accepts the same set of sentences fromW asG, and for each of them produces the same parse trees. The set of words W is obtained from a piece of text. Additionally, we assume that this operation is done “justin-time,” i.e., just before parsing the text. This application requires that this operation be done in an automatic and efficient way. After defining the problem in the general framework, we discuss the problem for context-free grammars (CFG), and give an efficient algorithm for it. We show that finding the smallest subgrammar for HPSGs is an NP-hard problem, and give an efficient algorithm that solves an easier, approximate version of the problem. We also discuss how the algorithm can be efficiently implemented.