Document Open Access Logo

Clique-Based Lower Bounds for Parsing Tree-Adjoining Grammars

Authors Karl Bringmann, Philip Wellnitz

PDF

File

Thumbnail PDF
PDF
LIPIcs.CPM.2017.12.pdf
  • Filesize: 0.51 MB
  • 14 pages

Document Identifiers

Subject Classification

Keywords
  • conditional lower bounds
  • k-Clique
  • parsing
  • tree-adjoining grammars

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

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.

Cite As Get BibTex

Karl Bringmann and Philip Wellnitz. Clique-Based Lower Bounds for Parsing Tree-Adjoining Grammars. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.CPM.2017.12

Author Details

Karl Bringmann
Philip Wellnitz

References

  1. Amir Abboud, Arturs Backurs, and Virginia Vassilevska Williams. If the current clique algorithms are optimal, so is Valiant’s parser. In Venkatesan Guruswami, editor, Proc. of the 56th IEEE Annual Symposium on Foundations of Computer Science (FOCS 2015), pages 98-117. IEEE Computer Society, 2015. URL: http://dx.doi.org/10.1109/FOCS.2015.16.
  2. Anne Abeillé. Parsing French with tree adjoining grammar: some linguistic accounts. In D. Vargha, editor, Proc. of the 12th Conf. on Computational Linguistics (COLING 1988), pages 7-12. Assoc. for Computational Linguistics, 1988. URL: http://dx.doi.org/10.3115/991635.991637.
  3. Arturs Backurs, Nishanth Dikkala, and Christos Tzamos. Tight hardness results for maximum weight rectangles. In I. Chatzigiannakis, M. Mitzenmacher, Y. Rabani, and D. Sangiorgi, editors, Proc. of the 43rd Int'l Colloquium on Automata, Languages, and Programming (ICALP 2016), volume 55 of LIPIcs, pages 81:1-81:13. Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2016. URL: http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.81.
  4. Arturs Backurs and Christos Tzamos. Improving Viterbi is hard: Better runtimes imply faster clique algorithms, 2016. URL: http://arxiv.org/abs/1607.04229.
  5. Karl Bringmann, Allan Grønlund, and Kasper Green Larsen. A dichotomy for regular expression membership testing, 2016. URL: http://arxiv.org/abs/1611.00918.
  6. Yi-Jun Chang. Hardness of RNA folding problem with four symbols. In Roberto Grossi and Moshe Lewenstein, editors, Proc. of the 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016), volume 54 of LIPIcs, pages 13:1-13:12. Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2016. URL: http://dx.doi.org/10.4230/LIPIcs.CPM.2016.13.
  7. David Chiang and Alexander Koller, editors. Proc. of the 12th International Workshop on Tree Adjoining Grammars and Related Formalisms (TAG+12). ACL, 2016. URL: http://www.aclweb.org/anthology/W16-33.
  8. John Cocke and Jacob T. Schwartz. Programming languages and their compilers: Preliminary notes. Technical report, Courant Institute of Mathematical Sciences, New York University, 1970. URL: http://www.softwarepreservation.org/projects/FORTRAN/CockeSchwartz_ProgLangCompilers.pdf.
  9. Vera Demberg, Frank Keller, and Alexander Koller. Incremental, predictive parsing with psycholinguistically motivated tree-adjoining grammar. Comput. Ling., 39(4):1025-1066, 2013. URL: http://dx.doi.org/10.1162/COLI_a_00160.
  10. Christy Doran, Dania Egedi, Beth Ann Hockey, Bangalore Srinivas, and Martin Zaidel. XTAG system: a wide coverage grammar for English. In Yorick Wilks, editor, Proc. of the 15th Conf. on Computational Linguistics (COLING 1994), pages 922-928. ACL, 1994. URL: http://dx.doi.org/10.3115/991250.991297.
  11. Jay Earley. An efficient context-free parsing algorithm. Commun. ACM, 13(2):94-102, 1970. URL: http://dx.doi.org/10.1145/362007.362035.
  12. Friedrich Eisenbrand and Fabrizio Grandoni. On the complexity of fixed parameter clique and dominating set. Theor. Comput. Sci., 326(1-3):57-67, 2004. URL: http://dx.doi.org/10.1016/j.tcs.2004.05.009.
  13. Katherine Forbes, Eleni Miltsakaki, Rashmi Prasad, Anoop Sarkar, Aravind Joshi, and Bonnie Webber. D-LTAG system: Discourse parsing with a lexicalized tree-adjoining grammar. J. Log. Lang. Inf., 12(3):261-279, 2003. URL: http://dx.doi.org/10.1023/A:1024137719751.
  14. Aravind K. Joshi. Tree adjoining grammars: How much context-sensitivity is required to provide reasonable structural descriptions? In D. R. Dowty, L. Karttunen, and A. M. Zwicky, editors, Natural Language Processing: Psychological, Computational, and Theoretical Perspectives. CUP, 1985. URL: http://dx.doi.org/10.1017/cbo9780511597855.007.
  15. Aravind K. Joshi, Leon S. Levy, and Masako Takahashi. Tree adjunct grammars. J. Comput. Syst. Sci., 10(1):136-163, 1975. URL: http://dx.doi.org/10.1016/S0022-0000(75)80019-5.
  16. Aravind K. Joshi and Yves Schabes. Tree-adjoining grammars. In Grzegorz Rozenberg and Arto Salomaa, editors, Beyond Words, volume 3 of Handbook of Formal Languages, pages 69-123. Springer, 1997. URL: http://dx.doi.org/10.1007/978-3-642-59126-6_2.
  17. Tadao Kasami. An efficient recognition and syntax algorithm for context-free languages. Technical Report R-257, Coordinated Science Laboratory, University of Illinois, 1966. URL: http://hdl.handle.net/2142/74304.
  18. Lillian Lee. Fast context-free grammar parsing requires fast boolean matrix multiplication. J. ACM, 49(1):1-15, 2002. URL: http://dx.doi.org/10.1145/505241.505242.
  19. Jaroslav Nešetřil and Svatopluk Poljak. On the complexity of the subgraph problem. Comment. Math. Univ. Carolin., 26(2):415-419, 1985. URL: http://dml.cz/dmlcz/106381.
  20. Sanguthevar Rajasekaran and Shibu Yooseph. TAL recognition in O(M(N²)) time. J. Comput. Syst. Sci., 56(1):83-89, 1998. URL: http://dx.doi.org/10.1006/jcss.1997.1537.
  21. Philip Resnik. Probabilistic tree-adjoining grammar as a framework for statistical natural language processing. In Antonio Zampolli, editor, Proc, of the 14th Conf. on Computational Linguistics (COLING 1992), pages 418-424. ACL, 1992. URL: http://dx.doi.org/10.3115/992133.992135.
  22. Giorgio Satta. Tree-adjoining grammar parsing and boolean matrix multiplication. Comput. Ling., 20(2):173-191, June 1994. URL: http://dl.acm.org/citation.cfm?id=972525.972527.
  23. Yves Schabes and Aravind K. Joshi. An Earley-type parsing algorithm for tree adjoining grammars. In J. Hobbs, editor, Proc. of the 26th Annual Meeting of the Association for Computational Linguistics (ACL 1988), pages 258-269. ACL, 1988. URL: http://dx.doi.org/10.3115/982023.982055.
  24. Stuart M. Shieber and Yves Schabes. Synchronous tree-adjoining grammars. In H. Karlgren, editor, Proc. of the 13th Conf. on Computational Linguistics (COLING 1990), pages 253-258. ACL, 1990. URL: http://dx.doi.org/10.3115/991146.991191.
  25. Matthew Stone and Christine Doran. Sentence planning as description using tree adjoining grammar. In Philip R. Cohen and Wolfgang Wahlster, editors, Proc. of the 35th Annual Meeting of the Association for Computational Linguistics (ACL 1997), pages 198-205. ACL, 1997. URL: http://dx.doi.org/10.3115/976909.979643.
  26. Yasuo Uemura, Aki Hasegawa, Satoshi Kobayashi, and Takashi Yokomori. Tree adjoining grammars for RNA structure prediction. Theor. Comput. Sci., 210(2):277-303, 1999. URL: http://dx.doi.org/10.1016/S0304-3975(98)00090-5.
  27. Leslie G. Valiant. General context-free recognition in less than cubic time. J. Comput. Syst. Sci., 10(2):308-315, 1975. URL: http://dx.doi.org/10.1016/s0022-0000(75)80046-8.
  28. Virginia Vassilevska. Efficient algorithms for clique problems. Inf. Process. Lett., 109(4):254-257, 2009. URL: http://dx.doi.org/10.1016/j.ipl.2008.10.014.
  29. K. Vijay-Shankar and Aravind K. Joshi. Some computational properties of tree adjoining grammars. In W. C. Mann, editor, Proc. of the 23rd Annual Meeting of the Association for Computational Linguistics (ACL 1985), pages 82-93. ACL, 1985. URL: http://dx.doi.org/10.3115/981210.981221.
  30. K. Vijay-Shanker and Aravind K. Joshi. Feature structures based tree adjoining grammars. In Dénes Vargha, editor, Proc. of the 12th Conf. on Computational Linguistics (COLING 1988), pages 714-719. ACL, 1988. URL: http://dx.doi.org/10.3115/991719.991783.
  31. Daniel H. Younger. Recognition and parsing of context-free languages in time n³. Inf. Control, 10(2):189-208, 1967. URL: http://dx.doi.org/10.1016/S0019-9958(67)80007-X.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact