eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-06-30
12:1
12:14
10.4230/LIPIcs.CPM.2017.12
article
Clique-Based Lower Bounds for Parsing Tree-Adjoining Grammars
Bringmann, Karl
Wellnitz, Philip
Tree-adjoining grammars are a generalization of context-free grammars that are well suited to model human languages and are thus popular in computational linguistics. In the tree-adjoining grammar recognition problem, given a grammar G and a string s of length n, the task is to decide whether s can be obtained from G. Rajasekaran and Yooseph’s parser (JCSS’98) solves this problem in time O(n^2w), where w < 2.373 is the matrix multiplication exponent. The best algorithms avoiding fast matrix multiplication take time O(n^6). The first evidence for hardness was given by Satta (J. Comp. Linguist.’94): For a more general parsing problem, any algorithm that avoids fast matrix multiplication and is significantly faster than O(|G|·n^6) in the case of |G| = Theta(n^12) would imply a breakthrough for Boolean matrix multiplication. Following an approach by Abboud et al. (FOCS’15) for context-free grammar recognition, in this paper we resolve many of the disadvantages of the previous lower bound. We show that, even on constant-size grammars, any improvement on Rajasekaran and Yooseph’s parser would imply a breakthrough for the k-Clique problem. This establishes tree-adjoining grammar parsing as a practically relevant problem with the unusual running time of n^2w , up to lower order factors.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol078-cpm2017/LIPIcs.CPM.2017.12/LIPIcs.CPM.2017.12.pdf
conditional lower bounds
k-Clique
parsing
tree-adjoining grammars