License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2017.12
URN: urn:nbn:de:0030-drops-73329
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7332/
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Bringmann, Karl ; Wellnitz, Philip

Clique-Based Lower Bounds for Parsing Tree-Adjoining Grammars

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Abstract

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.

BibTeX - Entry

@InProceedings{bringmann_et_al:LIPIcs:2017:7332,
  author =	{Karl Bringmann and Philip Wellnitz},
  title =	{{Clique-Based Lower Bounds for Parsing Tree-Adjoining Grammars}},
  booktitle =	{28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
  pages =	{12:1--12:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-039-2},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{78},
  editor =	{Juha K{\"a}rkk{\"a}inen and Jakub Radoszewski and Wojciech Rytter},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7332},
  URN =		{urn:nbn:de:0030-drops-73329},
  doi =		{10.4230/LIPIcs.CPM.2017.12},
  annote =	{Keywords: conditional lower bounds, k-Clique, parsing, tree-adjoining grammars}
}

Keywords: conditional lower bounds, k-Clique, parsing, tree-adjoining grammars
Collection: 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)
Issue Date: 2017
Date of publication: 30.06.2017

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