## Tree Insertion Grammar: A Cubic-Time, Parsable Formalism that Lexicalizes Context-Free Grammar without Changing the Trees Produced (1994)

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Venue: | Computational Linguistics |

Citations: | 80 - 1 self |

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@ARTICLE{Schabes94treeinsertion,

author = {Yves Schabes and Richard C. Waters},

title = {Tree Insertion Grammar: A Cubic-Time, Parsable Formalism that Lexicalizes Context-Free Grammar without Changing the Trees Produced},

journal = {Computational Linguistics},

year = {1994},

volume = {21}

}

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### Abstract

this paper, we study the problem of lexicalizing context-free grammars and show that it enables faster processing. In previous attempts to take advantage of lexicalization, a variety of lexicalization procedures have been developed that convert context-free grammars (CFGs) into equivalent lexicalized grammars. However, these procedures typically suffer from one or more of the following problems

### Citations

1360 | Head-Driven Phrase Structure Grammar - Pollard, Sag - 1994 |

702 | An efficient context-free parsing algorithm
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Citation Context ...487sComputational Linguistics Volume 21, Number 4 S A B a A S* D,I. b Figure 8 An auxiliary tree and its textual representation. ,1__ 4. 2 ,4 S ~A 5 6 7 "A---~"D "b LeftAux(, 1) Subst(,=-= 6) Foot(, 8) (Earley 1970-=-) with bottom-up recognition. The algorithm is a general recognizer for TIGs, which requires no condition on the grammar. 6 4.1 An Earley-Style Cubic-Time Parser For TIG Notation. Suppose that G = (G,... |

550 | Lexicalfunctional grammar: A formal system for grammatical representation - Bresnan, Kaplan - 1982 |

479 | Generalized Phrase Structure Grammar - Gazdar, Klein, et al. - 1985 |

336 |
Introduction to Formal Language Theory
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Citation Context ...proof of the fact that TIG strongly lexicalizes CFG. The proof is based on a lexicalization procedure related to the lexicalization procedure used to create Greibach normal form (GNF) as presented in =-=Harrison 1978-=-. 5.1.1 Lemmas. Our procedure relies on the following four lemmas. The first lemma converts CFGs into a very restricted form of TIG. The next three lemmas describe ways that TIGs can be transformed wi... |

172 | Principles and implementation of deductive parsing - Shieber, Schabes, et al. - 1995 |

162 |
Mathematical and Computational Aspects of Lexicalized Grammars
- Schabes
- 1990
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Citation Context ...t does not produce the right trees. Strong lexicalization that preserves the trees derived is possible using context-sensitive formalisms such as tree adjoining grammar (TAG) (Joshi and Schabes 1992; =-=Schabes 1990-=-). However, these context-sensitive formalisms entail larger computation costs than CFGs--O(n6)-time in the case of TAG (Vijay-Shanker and Joshi 1985), instead of O(n 3) for CFG. Tree Insertion Gramma... |

144 | Characterizing Mildly Context-Sensitive Grammar Formalisms - Weir - 1988 |

128 | Efficient Parsing for Natural Language. A fast algorithm for practical systems - Tomita - 1986 |

118 | Parsing strategies with `lexicalized' grammars: Application to Tree Adjoining Grammars - Schabes, Abeille, et al. - 1988 |

114 | A study of tree adjoining grammars - Vijay-Shanker - 1987 |

111 | An Alternative Conception of TreeAdjoining Derivation - Schabes, Shieber - 1994 |

103 |
How much context-sensitivity is necessary for characterizing structural descriptions — Tree Adjoining Grammars
- Joshi
- 1985
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Citation Context ...adjoining grammar (TAG) (Joshi and Schabes 1992; Schabes 1990). However, these context-sensitive formalisms entail larger computation costs than CFGs--O(n6)-time in the case of TAG (Vijay-Shanker and =-=Joshi 1985-=-), instead of O(n 3) for CFG. Tree Insertion Grammar (TIG) is a compromise between CFG and TAG that combines the efficiency of the former with the strong lexicalizing power of the latter. As discussed... |

93 |
Tree adjoining grammars and lexicalized grammars
- Joshi, Schabes
- 1991
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Citation Context ...ammar can be fast, but it does not produce the right trees. Strong lexicalization that preserves the trees derived is possible using context-sensitive formalisms such as tree adjoining grammar (TAG) (=-=Joshi and Schabes 1992-=-; Schabes 1990). However, these context-sensitive formalisms entail larger computation costs than CFGs--O(n6)-time in the case of TAG (Vijay-Shanker and Joshi 1985), instead of O(n 3) for CFG. Tree In... |

84 |
An improved context-free recognizer
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Citation Context ...e efficiency of the TIG parser can be improved. Parsingthatislinearinthegrammarsize. The time complexity of the parser can be reduced from O(IGI2n 3) to O(IGIn 3) by using the techniques described in =-=Graham et al. 1980-=-). This improvement is very important, because IG[ typically is much larger than n for natural language applications. The speedup can be achieved by altering the parser in two ways. The prediction rul... |

71 | Combinatory Grammars and Parasitic Gaps", Natural Language and Linguistic Theory 5 - Steedman - 1987 |

68 |
Radical lexicalism
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Citation Context ... illustrating the increased use of lexical information are: lexical rules in LFG (Kaplan and Bresnan 1983), GPSG (Gazdar et al. 1985), HPSG (Pollard and Sag 1987), Categorial Grammars (Steedman 1987; =-=Karttunen 1986-=-), some versions of GB theory (Chomsky 1981), and Lexicon-Grammars (Gross 1984). @ 1995 Association for Computational LinguisticssComputational Linguistics Volume 21, Number 4 and Rosenkrantz (1967) o... |

67 | On categorial and phrase structure grammars - Bar-Hillel, Gaifman, et al. - 1960 |

61 | Deducing linguistic structure from the statistics of large corpora - Brill, Magerman, et al. - 1990 |

58 | Parsing Some Constrained Grammar Formalisms - Vijay-Shanker, Weir - 1993 |

52 |
Information-Based Syntax and Semantics. Vol 1: Fundamentals. csli
- Pollard, Sag
- 1987
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Citation Context ...chabes/waters@merl.com. 1 Some of the linguistic formalisms illustrating the increased use of lexical information are: lexical rules in LFG (Kaplan and Bresnan 1983), GPSG (Gazdar et al. 1985), HPSG (=-=Pollard and Sag 1987-=-), Categorial Grammars (Steedman 1987; Karttunen 1986), some versions of GB theory (Chomsky 1981), and Lexicon-Grammars (Gross 1984). @ 1995 Association for Computational LinguisticssComputational Lin... |

43 | Stochastic Lexicalized Context-Free Grammar
- Schabes
- 1993
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Citation Context ... to record whether adjunction has occurred at a given node. Third, one can introduce stochastic parameters controlling the probabilities with which particular substitutions and adjunctions occur (see =-=Schabes and Waters 1993-=-b). Fourth, and of particular importance in the current paper, one can require that a TIG be lexicalized. Definition 7 [LTIG] A lexicalized tree insertion grammar (LTIG) 4 (G, NT, L A, S) is a TIG whe... |

35 |
Combinatory grammars and parasitic gaps
- Steedman
- 1987
(Show Context)
Citation Context ...stic formalisms illustrating the increased use of lexical information are: lexical rules in LFG (Kaplan and Bresnan 1983), GPSG (Gazdar et al. 1985), HPSG (Pollard and Sag 1987), Categorial Grammars (=-=Steedman 1987-=-; Karttunen 1986), some versions of GB theory (Chomsky 1981), and Lexicon-Grammars (Gross 1984). @ 1995 Association for Computational LinguisticssComputational Linguistics Volume 21, Number 4 and Rose... |

33 |
Lexicon-grammar and the syntactic analysis of French
- Gross
- 1984
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Citation Context ...Kaplan and Bresnan 1983), GPSG (Gazdar et al. 1985), HPSG (Pollard and Sag 1987), Categorial Grammars (Steedman 1987; Karttunen 1986), some versions of GB theory (Chomsky 1981), and Lexicon-Grammars (=-=Gross 1984-=-). @ 1995 Association for Computational LinguisticssComputational Linguistics Volume 21, Number 4 and Rosenkrantz (1967) often produce very large output grammars--so large that they can be awkward or ... |

25 | A new normal-form theorem for context-free phrase structure grammars - Greibach - 1965 |

19 | The valid prefix property and left to right parsing of tree-adjoining grammar - Schabes - 1991 |

13 | The systematic construction of earley parsers: Application to the production of o(n6) earley parsers for tree adjoining grammars
- Lang
- 1990
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Citation Context ...ine. Since this intersection is not a regular language, L cannot be a regular language. 4. Parsing TIG Since TIG is a restricted case of tree-adjoining grammar (TAG), standard O(n6)-time TAG parsers (=-=Lang 1990-=-; Schabes 1991; Vijay-Shanker 1987; Vijay-Shanker and Weir 1993; Vijay-Shanker and Joshi 1985) can be used for parsing TIG. Further, they can be easily optimized to require at most O(n4)-time when app... |

13 |
An Animated Online Community with Artificial Agents and Spoken Interaction
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- 1994
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Citation Context ...ons. 8 The eighth grammar is a CFG grammar used in the natural language processing component of a simple interactive computer environment. It supports conversation with an animated robot called Mike (=-=Rich et al. 1994-=-a and 1994b). The grammars are all finitely ambiguous and none generates the empty string. The Tomita III grammar contains an empty rule. The relative size and complexity of the grammars is indicated ... |

13 |
Characterizing derivation trees of context free grammars through a generahzatlon f finite automata theory J Computer and Syst Scis 1
- THATCHER
- 1967
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Citation Context ...of a grammar is the set of all paths from root to frontier in the trees generated by the grammar. The path set is a set of strings in (~. U NT)*. CFGs have path sets that are regular languages (RLs) (=-=Thatcher 1971-=-). In contrast, TAGs have path sets that are context-free languages (CFLs) (Weir 1988). 486sSchabes and Waters Tree Insertion Grammar Figure 7 A TIG with a context-free path set. A S a The fact that t... |

8 | Matrix equations and normal forms for context-free grammars - ROSENKRANTZ - 1967 |

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- Schabes, Waters
- 1993
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Citation Context ... to record whether adjunction has occurred at a given node. Third, one can introduce stochastic parameters controlling the probabilities with which particular substitutions and adjunctions occur (see =-=Schabes and Waters 1993-=-b). Fourth, and of particular importance in the current paper, one can require that a TIG be lexicalized. Definition 7 [LTIG] A lexicalized tree insertion grammar (LTIG) 4 (G, NT, L A, S) is a TIG whe... |

6 | Demonstration of an Interactive Environment for Collaboration and Learning - Rich, Waters, et al. - 1994 |

4 |
Demonstration of an interactive multimedia environment
- Rich, Waters, et al.
- 1994
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Citation Context ...ons. 8 The eighth grammar is a CFG grammar used in the natural language processing component of a simple interactive computer environment. It supports conversation with an animated robot called Mike (=-=Rich et al. 1994-=-a and 1994b). The grammars are all finitely ambiguous and none generates the empty string. The Tomita III grammar contains an empty rule. The relative size and complexity of the grammars is indicated ... |

2 | Lexicalized TAGs, parsing and lexicons - Bishop, Cote, et al. - 1989 |

1 |
The predictive analyzer and context-free grammars
- Abbott, Kuno
- 1965
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Citation Context ...rammar. This is due to loss of information when the same rule is derived in more than one way by the GNF procedure. Ambiguity can be retained simply by retaining any duplicate rules that are derived (=-=Abbott and Kuno 1965-=-). Third, the GNF procedure changes the trees produced. This is an essential difference and cannot be avoided. However, as shown by Abbott and Kuno (1965), it is possible to transform parse trees crea... |

1 | An Efficient Context-Free Computational Linguistics Volume 21, Number 4 Parsing Algorithm. Doctoral dissertation - Earley - 1968 |