## A Tree Transducer Model for Synchronous Tree-Adjoining Grammars

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@MISC{Maletti_atree,

author = {Andreas Maletti},

title = {A Tree Transducer Model for Synchronous Tree-Adjoining Grammars},

year = {}

}

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### Abstract

A characterization of the expressive power of synchronous tree-adjoining grammars (STAGs) in terms of tree transducers (or equivalently, synchronous tree substitution grammars) is developed. Essentially, a STAG corresponds to an extended tree transducer that uses explicit substitution in both the input and output. This characterization allows the easy integration of STAG into toolkits for extended tree transducers. Moreover, the applicability of the characterization to several representational and algorithmic problems is demonstrated. 1

### Citations

651 | Synchronous Tree Adjoining Grammars - Sheiber, Schabes - 1990 |

381 | A hierarchical phrase-based model for statistical machine translation
- Chiang
- 2005
(Show Context)
Citation Context ... dependency problems, Shieber and Schabes (1990) and Shieber (2007) suggest a stronger model called synchronous tree-adjoining grammar (STAG), which in addition to the substitution operation of STSG (=-=Chiang, 2005-=-) also has an adjoining operation. Let us recall the model in some detail. A treeadjoining grammar essentially is a regular tree grammar (Gécseg and Steinby, 1984; Gécseg and t3 DT les NP N bonbons de... |

237 |
Tree Automata. Akadémiai Kiado
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- 1984
(Show Context)
Citation Context ... too weak as a syntax-based model, but found use in the string-based setting. Top-down tree transducers (Rounds, 1970; Thatcher, 1970) have been heavily investigated in the formal language community (=-=Gécseg and Steinby, 1984-=-; Gécseg and Steinby, 1997), but as argued by Shieber (2004) they are still too weak for syntax-based machine translation. Instead Shieber (2004) proposes synchronous tree substitution grammars (STSGs... |

153 | Better k-best parsing
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(Show Context)
Citation Context ... of the STAGs. Such properties are especially valuable when we simulate STAG in toolkits for XTT. A second standard algorithm that easily translates is the algorithm computing the n-best derivations (=-=Huang and Chiang, 2005-=-). Clearly, the nbest derivation algorithm does not consider a particular input or output tree. Since the derivations of the XTT match the derivations of the STAG (in the former the input and output a... |

152 |
The Theory of Parsing, Translation and Compiling
- Aho, Ullman
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(Show Context)
Citation Context ...roduction Machine translation has seen a multitude of formal translation models. Here we focus on syntaxbased (or tree-based) models. One of the oldest models is the synchronous context-free grammar (=-=Aho and Ullman, 1972-=-). It is clearly too weak as a syntax-based model, but found use in the string-based setting. Top-down tree transducers (Rounds, 1970; Thatcher, 1970) have been heavily investigated in the formal lang... |

136 |
Tree languages
- Gécseg, Steinby
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(Show Context)
Citation Context ...d model, but found use in the string-based setting. Top-down tree transducers (Rounds, 1970; Thatcher, 1970) have been heavily investigated in the formal language community (Gécseg and Steinby, 1984; =-=Gécseg and Steinby, 1997-=-), but as argued by Shieber (2004) they are still too weak for syntax-based machine translation. Instead Shieber (2004) proposes synchronous tree substitution grammars (STSGs) and develops an equivale... |

121 |
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Citation Context ...t trees returned by n-best derivation algorithm. Finally, let us consider an algorithm that can be obtained for STAG by developing it for XTT using explicit substitution. We will develop a BARHILLEL (=-=Bar-Hillel et al., 1964-=-) construction for STAG. Thus, given a STAG G and a recognizable tree language L, we want to construct a STAG G ′ such that τG ′ = {(t, u) | (t, u) ∈ τG, t ∈ L} . In other words, we take the tree tran... |

121 |
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- Rounds
- 1970
(Show Context)
Citation Context ...the oldest models is the synchronous context-free grammar (Aho and Ullman, 1972). It is clearly too weak as a syntax-based model, but found use in the string-based setting. Top-down tree transducers (=-=Rounds, 1970-=-; Thatcher, 1970) have been heavily investigated in the formal language community (Gécseg and Steinby, 1984; Gécseg and Steinby, 1997), but as argued by Shieber (2004) they are still too weak for synt... |

110 |
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- Engelfriet, Vogler
- 1985
(Show Context)
Citation Context ...e and two embedded tree transducers (instead of two tree homomorphisms). Such embedded tree transducers (Shieber, 2006) are particular macro tree transducers (Courcelle and Franchi-Zannettacci, 1982; =-=Engelfriet and Vogler, 1985-=-). In this contribution, we try to unify the picture even further. We will develop a tree transducer model that can simulate STAGs. It turns out that the adjunction operation of an STAG can be explain... |

107 | Training tree transducers
- Graehl, Knight
- 2004
(Show Context)
Citation Context ... substitution grammars (STSGs) and develops an equivalent bimorphism (Arnold and Dauchet, 1982) characterization. This characterization eventually led to the rediscovery of extended tree transducers (=-=Graehl and Knight, 2004-=-; Knight and Graehl, 2005; Graehl et al., 2008), which are essentially as powerful as STSG. They had been studied already by Arnold and Dauchet (1982) in the form of bimorphisms, but received little a... |

65 |
An overview of probabilistic tree transducers for natural language processing
- Knight, Graehl
- 2005
(Show Context)
Citation Context ...TSGs) and develops an equivalent bimorphism (Arnold and Dauchet, 1982) characterization. This characterization eventually led to the rediscovery of extended tree transducers (Graehl and Knight, 2004; =-=Knight and Graehl, 2005-=-; Graehl et al., 2008), which are essentially as powerful as STSG. They had been studied already by Arnold and Dauchet (1982) in the form of bimorphisms, but received little attention until rediscover... |

57 |
Attribute grammars and recursive program schemes I
- Courcelle, Franchi-Zannettacci
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(Show Context)
Citation Context ...se they consist of a regular tree language and two embedded tree transducers (instead of two tree homomorphisms). Such embedded tree transducers (Shieber, 2006) are particular macro tree transducers (=-=Courcelle and Franchi-Zannettacci, 1982-=-; Engelfriet and Vogler, 1985). In this contribution, we try to unify the picture even further. We will develop a tree transducer model that can simulate STAGs. It turns out that the adjunction operat... |

32 | The power of extended top-down tree transducers
- Maletti, Graehl, et al.
- 2009
(Show Context)
Citation Context ...been studied first by Arnold and Dauchet (1982) in a purely theoretic setting, but were later applied in, for example, machine translation (Knight and Graehl, 2005; Knight, 2007; Graehl et al., 2008; =-=Graehl et al., 2009-=-). Their popularity in machine translation is due to Shieber (2004), in which it is shown that extended tree transducers are essentially (up to a relabeling) as expressive as synchronous tree substitu... |

27 | Capturing practical natural language transformations
- Knight
(Show Context)
Citation Context ...nsformation. Such transducers have been studied first by Arnold and Dauchet (1982) in a purely theoretic setting, but were later applied in, for example, machine translation (Knight and Graehl, 2005; =-=Knight, 2007-=-; Graehl et al., 2008; Graehl et al., 2009). Their popularity in machine translation is due to Shieber (2004), in which it is shown that extended tree transducers are essentially (up to a relabeling) ... |

22 | Synchronous grammars as tree transducers - Shieber |

16 |
M.: Morphismes et bimorphismes d’arbres. Theor
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- 1982
(Show Context)
Citation Context ...d by Shieber (2004) they are still too weak for syntax-based machine translation. Instead Shieber (2004) proposes synchronous tree substitution grammars (STSGs) and develops an equivalent bimorphism (=-=Arnold and Dauchet, 1982-=-) characterization. This characterization eventually led to the rediscovery of extended tree transducers (Graehl and Knight, 2004; Knight and Graehl, 2005; Graehl et al., 2008), which are essentially ... |

12 | An introduction to synchronous grammars - Chiang - 2006 |

2 |
Association for Computational Linguistics. See also (Graehl et al
- Graehl, Knight, et al.
- 2008
(Show Context)
Citation Context ...ivalent bimorphism (Arnold and Dauchet, 1982) characterization. This characterization eventually led to the rediscovery of extended tree transducers (Graehl and Knight, 2004; Knight and Graehl, 2005; =-=Graehl et al., 2008-=-), which are essentially as powerful as STSG. They had been studied already by Arnold and Dauchet (1982) in the form of bimorphisms, but received little attention until rediscovered. Shieber (2007) cl... |

2 | Training tree transducers. Computational Linguistics 34:391–427 - Graehl, Knight, et al. - 2008 |