## THE POWER OF EXTENDED TOP-DOWN TREE TRANSDUCERS

Citations: | 30 - 22 self |

### BibTeX

@MISC{Maletti_thepower,

author = {Andreas Maletti and Jonathan Graehl and Mark Hopkins and Kevin Knight},

title = {THE POWER OF EXTENDED TOP-DOWN TREE TRANSDUCERS},

year = {}

}

### OpenURL

### Abstract

Extended top-down tree transducers (transducteurs generalises descendants [Arnold, Dauchet: Bi-transductions de forets. ICALP'76. Edinburgh University Press. 1976]) received renewed interest in the field of Natural Language Processing. Here those transducers are extensively and systematically studied. Their main properties are identified and their relation to classical top-down tree transducers is exactly characterized. The obtained properties completely explain the Hasse diagram of the induced classes of tree transformations. In addition, it is shown that most interesting classes of transformations computed by extended top-down tree transducers are not closed under composition.

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(Show Context)
Citation Context ... [14], • tree bimorphisms [2], and various models with synchronization (e.g., [24]). Computational linguists had returned to using simpler transducer models based on strings. Finite state transducers =-=[19]-=- are straightforward to write down, and it is easy to add probabilities to them and to train them on large quantities of linguistic data. The designer’s goal is to capture a set of linguistic pairs of... |

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Citation Context ...egrated. For example, top-down tree transducers were devised by Thatcher [27] and Rounds [25], the latter of whom wanted to model the transformational grammars of natural language proposed by Chomsky =-=[4]-=- in the 1960s. For the most part, the fields subsequently went separate ways. By the 1990s, automata researchers had invented new models based on other concerns. Among these, we find: • bottom-up tree... |

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Citation Context ...erarchy, composition closure AMS subject classifications. 68Q45 (primary), 68T50 (secondary) 1. Introduction. The fields of tree automata (see [16, 17] for surveys) and computational linguistics (see =-=[23, 20]-=- for surveys) were once tightly integrated. For example, top-down tree transducers were devised by Thatcher [27] and Rounds [25], the latter of whom wanted to model the transformational grammars of na... |

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Citation Context ...omata (see [16, 17] for surveys) and computational linguistics (see [23, 20] for surveys) were once tightly integrated. For example, top-down tree transducers were devised by Thatcher [27] and Rounds =-=[25]-=-, the latter of whom wanted to model the transformational grammars of natural language proposed by Chomsky [4] in the 1960s. For the most part, the fields subsequently went separate ways. By the 1990s... |

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Citation Context ...e or impossible. To address these drawbacks, a generalization of top-down tree transducers, called extended top-down tree transducers, was originally conceived by [25] and has been further pursued by =-=[6, 1, 18, 21]-=-. The extended transducer does not suffer from the representational inadequacies outlined above, and thus has emerged as a promising candidate for use in linguistic tasks. Rules in an extended transdu... |

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Citation Context ...e or impossible. To address these drawbacks, a generalization of top-down tree transducers, called extended top-down tree transducers, was originally conceived by [25] and has been further pursued by =-=[6, 1, 18, 21]-=-. The extended transducer does not suffer from the representational inadequacies outlined above, and thus has emerged as a promising candidate for use in linguistic tasks. Rules in an extended transdu... |

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Citation Context ...elds of tree automata (see [16, 17] for surveys) and computational linguistics (see [23, 20] for surveys) were once tightly integrated. For example, top-down tree transducers were devised by Thatcher =-=[27]-=- and Rounds [25], the latter of whom wanted to model the transformational grammars of natural language proposed by Chomsky [4] in the 1960s. For the most part, the fields subsequently went separate wa... |

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Citation Context ...the 1990s, automata researchers had invented new models based on other concerns. Among these, we find: • bottom-up tree transducers [28] and attributed tree transducers [15], • macro tree transducers =-=[5, 13]-=- and modular tree transducers [14], • tree bimorphisms [2], and various models with synchronization (e.g., [24]). Computational linguists had returned to using simpler transducer models based on strin... |

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Citation Context ...quently went separate ways. By the 1990s, automata researchers had invented new models based on other concerns. Among these, we find: • bottom-up tree transducers [28] and attributed tree transducers =-=[15]-=-, • macro tree transducers [5, 13] and modular tree transducers [14], • tree bimorphisms [2], and various models with synchronization (e.g., [24]). Computational linguists had returned to using simple... |

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Citation Context ...e transformations computed by xtt R . All edges are directed to the right or upward. Let us recall that ln-TOP and l-TOP R are closed under composition. Both composition constructions can be found in =-=[3]-=-, though the results trace back to [9]. Instead of linear tdttR , Baker and Engelfriet investigated linear bottom-up tree transducers [28]. However, Engelfriet [10, Theorem 2.8] showed that linear bot... |

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Citation Context ...nite look-ahead, (X2) deep attachment of variables, and (X3) infinitely many outputs for one input. Actually, finite look-ahead is a weak form of the bottom-up property: checking followed by deletion =-=[9]-=-. Deep attachment of variables will allow us to specify local rotations easily. Finally, the last property makes it possible to have nondeterministic choice independent of input symbols. It is known t... |

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Citation Context ...le of a local rotation. the model powerful enough to capture what is observed in empirical translation data? Other concerns include representational succinctness and computational complexity. Shieber =-=[26]-=- and others have argued that top-down tree transducers [27, 25] are generally inadequate for linguistic tasks because they cannot straightforwardly model local rotation, i.e., the reordering of tree c... |

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Citation Context ...e or impossible. To address these drawbacks, a generalization of top-down tree transducers, called extended top-down tree transducers, was originally conceived by [25] and has been further pursued by =-=[6, 1, 18, 21]-=-. The extended transducer does not suffer from the representational inadequacies outlined above, and thus has emerged as a promising candidate for use in linguistic tasks. Rules in an extended transdu... |

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Citation Context ...gnizable tree languages are closed under OI-substitution [16, Theorem II.4.6]. Next, we recall the central concept of an extended top-down tree transducer [6, 1, 18, 21] (we follow the definitions of =-=[22]-=-). We immediately add regular look-ahead [10] to the device in order to present a model that generalizes all required transducing devices. Let Q be a finite set, Σ and ∆ be ranked alphabets, and T ⊆ T... |

17 |
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Citation Context ... tree transducers [28] and attributed tree transducers [15], • macro tree transducers [5, 13] and modular tree transducers [14], • tree bimorphisms [2], and various models with synchronization (e.g., =-=[24]-=-). Computational linguists had returned to using simpler transducer models based on strings. Finite state transducers [19] are straightforward to write down, and it is easy to add probabilities to the... |

10 |
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(Show Context)
Citation Context |

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(Show Context)
Citation Context ...e transformations that contain l-XTOP and are closed under composition. An example of such a class is the class l-XMBOT of transformations computed by linear extended multi bottom-up tree transducers =-=[12]-=-. At this point, we already proved that most classes of Fig. 4.5 are not closed under composition. In addition, we know [10, Corollary 2.4] that TOP R is not closed under composition. So, it only rema... |

6 |
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(Show Context)
Citation Context ...rmed (as it is the case for TOP [11]) or whether L n = L n+1 for some n (as it is the case, e.g., for (i) nl-TOP 1 [9] or (ii) l-TOP 2 [9] or (iii) B(lne-HOM, lne-HOM) 2 [2] or (iv) B(l-HOM, l-HOM) 4 =-=[7, 8]-=-). In addition, it would be interesting to (syntactically) identify classes L such that ln-TOP ⊂ L ⊂ ln-XTOP and L is closed under composition. We showed (see Theorem 5.2) that no such class of transf... |

1 |
et bimorphismes d’arbres., Theor
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(Show Context)
Citation Context ...data, and to understand the formal properties of those models. Several interesting problems remain open. In the light of composition hierarchy results for tree transformations computed by bimorphisms =-=[2]-=- and top-down tree transducers [11], it is interesting to study the composition closure of a class L of transformations computed by extended tree transducers. We showed that L ⊂ L 2 where L 2 = L ; L ... |

1 | de for^ets. Bimorphismes de magmo des, These d'Etat, Universite de - Transductions - 1977 |

1 |
tree transducers with regular look-ahead
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(Show Context)
Citation Context ...-copying) top-down tree transducers do not have these features. They can only be simulated at the expense of either (a) adding them explicitly (e.g., top-down tree transducers with regular look-ahead =-=[10]-=-) or (b) dropping the linearity condition. We demonstrate under which circumstances these formal properties make extended transducers more expressive than their non-extended counterparts. In fact, we ... |

1 |
de forêts. Bimorphismes de magmoïdes, Thèse d’ État, Université de
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(Show Context)
Citation Context ...rmed (as it is the case for TOP [11]) or whether L n = L n+1 for some n (as it is the case, e.g., for (i) nl-TOP 1 [9] or (ii) l-TOP 2 [9] or (iii) B(lne-HOM, lne-HOM) 2 [2] or (iv) B(l-HOM, l-HOM) 4 =-=[7, 8]-=-). In addition, it would be interesting to (syntactically) identify classes L such that ln-TOP ⊂ L ⊂ ln-XTOP and L is closed under composition. We showed (see Theorem 5.2) that no such class of transf... |