## The power of extended top-down tree transducers (2008)

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Venue: | SIAM J. COMPUT |

Citations: | 17 - 15 self |

### BibTeX

@ARTICLE{Maletti08thepower,

author = {Andreas Maletti},

title = { The power of extended top-down tree transducers},

journal = {SIAM J. COMPUT},

year = {2008}

}

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### Abstract

Unfortunately, the class of transformations computed by linear extended top-down tree transducers with regular look-ahead is not closed under composition. It is shown that the class of transformations computed by certain linear bimorphisms coincides with the previously mentioned class. Moreover, it is demonstrated that every linear epsilon-free extended top-down tree transducer with regular look-ahead can be implemented by a linear multi bottom-up tree transducer. The class of transformations computed by the latter device is shown to be closed under composition, and to be included in the composition of the class of transformations computed by top-down tree transducers with itself. More precisely, it constitutes the composition closure of the class of transformations computed by nite-copying top-down tree transducers.

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Citation Context ...ansducer, composition, bimorphism, natural language processing, tree transformation 1. Introduction The top-down tree transducer (tdtt) was introduced in [1,2] and intensively studied thereafter (see =-=[3,4]-=- for a survey). It was originally motivated from natural language processing [5] and syntax-directed semantics [6], but was later successfully applied to problems as diverse as: functional programming... |

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Citation Context ...on and is included in the composition of the class of transformations realized by top-down tree transducers with itself. 1 Introduction Top-down tree transducers (for short: tdtts) were introduced in =-=[1, 2]-=- and intensively studied thereafter (see [3] for a survey). Those devices were originally motivated from syntax-directed semantics [4], but were later successfully applied to problems as diverse as: f... |

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Citation Context ...on and is included in the composition of the class of transformations realized by top-down tree transducers with itself. 1 Introduction Top-down tree transducers (for short: tdtts) were introduced in =-=[1, 2]-=- and intensively studied thereafter (see [3] for a survey). Those devices were originally motivated from syntax-directed semantics [4], but were later successfully applied to problems as diverse as: f... |

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Citation Context ...nitial state and t is the input tree. An extended tdtt may thus transform an input tree t into an output tree u if there exists an initial state q such that q(t) can be rewritten to u. It is shown in =-=[14]-=- that synchronized tree substitution grammars [15] are as powerful (upto relabeling) as bimorphisms (see survey [16]) of type (LC, LC) [14]. We first show that nondeleting and linear extended tdtts ar... |

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Citation Context ...s required in [25,31] to deterministically identify the root of the input tree. In [25] the root symbol is needed to show that deterministic mbutt are as powerful as deterministic tdttR . Compared to =-=[23,24]-=-, we disallow rules that do not consume any input symbol (epsilon rules). Essentially, an mbutt is a bottom-up tree transducer [32,10], in which states may have arbitrary rank. Let and Q be disjoint r... |

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Citation Context ...us recall the multi bottom-up tree transducer (mbutt; also called STA or S-transducteur ascendant) of [23{25,31]. We slightly adapt the model by omitting the special root symbol, which is required in =-=[25,31]-=- to deterministically identify the root of the input tree. In [25] the root symbol is needed to show that deterministic mbutt are as powerful as deterministic tdttR . Compared to [23,24], we disallow ... |

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Citation Context ...op-down tree transducers (for short: tdtts) were introduced in [1, 2] and intensively studied thereafter (see [3] for a survey). Those devices were originally motivated from syntax-directed semantics =-=[4]-=-, but were later successfully applied to problems as diverse as: functional programming [5]; analysis of cryptographic protocols [6]; and decidability of the first-order theory of ground rewriting [7]... |

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Citation Context ...se devices were originally motivated from syntax-directed semantics [4], but were later successfully applied to problems as diverse as: functional programming [5]; analysis of cryptographic protocols =-=[6]-=-; and decidability of the first-order theory of ground rewriting [7]. In particular, compositions of tdtts are considered in [8, 9]. In this paper we study compositions of extended tdtts, which were i... |

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Citation Context ...XTOP, and l{XTOP R are not closed under composition. 4. Multi Bottom-up Tree Transducer Next, let us recall the multi bottom-up tree transducer (mbutt; also called STA or S-transducteur ascendant) of =-=[23{25,31]-=-. We slightly adapt the model by omitting the special root symbol, which is required in [25,31] to deterministically identify the root of the input tree. In [25] the root symbol is needed to show that... |

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Citation Context ...here exists an initial state q such that q(t) can be rewritten to u. It is shown in [14] that synchronized tree substitution grammars [15] are as powerful (upto relabeling) as bimorphisms (see survey =-=[16]-=-) of type (LC, LC) [14]. We first show that nondeleting and linear extended tdtts are as powerful as bimorphisms of type (LC, LC), which thus shows that nondeleting and linear extended tdtts are as po... |

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Citation Context ...for a survey). It was originally motivated from natural language processing [5] and syntax-directed semantics [6], but was later successfully applied to problems as diverse as: functional programming =-=[7]-=-, analysis of cryptographic protocols [8], and decidability of the rst-order theory of ground rewriting [9]. Corresponding author. Address: Technische Universitat Dresden, 01062 Dresden, Germany. Emai... |

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Citation Context ...lities follow directly from (the proof of) Theorem 11 and Lemmata 12 and 13. 2 The following development of the relation of mbutt to nite-copying tdtts [26] is essentially due to an anonymous referee =-=[34]-=-. Roughly speaking, a tdtt is nite-copying if it processes each input subtree at most a bounded number of times. Formally, a tdtt M = (Q; ; ; I; R) is m-copying for some m 2 N if card(pos ?(u)) m for ... |

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Citation Context ...anguage processing. However, nondeleting and linear extended tdtt as well as linear extended tdtt with regular look-ahead [17] compute classes of transformations that are not closed under composition =-=[13,18,19]-=-. In essence, this requires us to consider either slightly more restricted classes or slightly larger classes. In this paper, we will follow a combination of both approaches; we rst restrict ourselves... |