Weighted extended top-down tree transducers (transducteurs généralisés descendants [Arnold, Dauchet: Bi-transductions de forêts. ICALP’76. Edinburgh University Press. 1976]) received renewed interest in the field of Natural Language Processing, where they are used in syntax-based machine translation. This survey presents the foundations for a theoretical analysis of weighted extended top-down t...

We argue that intelligible appeals to interlevel causes (top-down and bottom-up) can be understood, without remainder, as appeals to mechanistically mediated effects. Mechanistically mediated effects are hybrids of causal and constitutive relations, where the causal relations are exclusively intralevel. The idea of causation would have to stretch to the breaking point to accommodate interlevel ...

We consider the following tree-matching problem: Given labelled, ordered trees P and T, can P be obtained from T by deleting nodes. Deleting a node v entails removing all edges incident to v and, if v has a parent u, replacing the edges from u to v by edges from u to the children of v. The best known algorithm for this problem needs O(|T|·|leaves(P)|) time and O(|leaves(P)|·min{DT,·|leaves(T)|}...

Tree-structured neural networks (TSNN) are known to be universal ap-proximators that have easily derivable equivalent implementations as feed-forward neural networks with two hidden layers. What makes them particularly interesting for large-scale and real-time applications such as adaptive control is their ability to support eecient lazy evaluation by exploiting their hierarchical structure and...

We study the problem of how to learn tree transformations on a given regular tree domain from a finite sample of input-output examples. We assume that the target tree transformation can be defined by a deterministic top-down tree transducer with regular domain inspection (DTopIreg). An rpni style learning algorithm that solves this problem in polynomial time and with polynomially many examples ...

An ordered labeled tree is a tree which nodes are labeled and in which the left-to-right order among siblings is significant. Given two ordered labeled trees P and T , the constrained tree inclusion problem is to determine whether it is possible to obtain P from T by deleting degree-one or degreetwo nodes. G. Valiente proposed a bottom up algorithm which solves the problem in O(|P ||T |) time a...

This work is a study of the expressive power of unambiguity in the case of infinite trees. An automaton is called unambiguous if it has at most one accepting run on every input, the language of such an automaton is called an unambiguous language. It is known that not every regular language of infinite trees is unambiguous. Except that, very little is known about which regular tree languages are...

Long Short-Term Memory (LSTM) networks, a type of recurrent neural network with a more complex computational unit, have been successfully applied to a variety of sequence modeling tasks. In this paper we develop Tree Long Short-Term Memory (TREELSTM), a neural network model based on LSTM, which is designed to predict a tree rather than a linear sequence. TREELSTM defines the probability of a se...

Top-down tree transducers are a convenient formalism for describing tree transformations. They can be equipped with regular look-ahead, which allows them to inspect a subtree before processing it. In certain cases, such a look-ahead can be avoided and the transformation can be realized by a transducer without look-ahead. Removing the look-ahead from a transducer, if possible, is technically hig...

A weighted tree transformation is a function : T T ! A where T and T are the sets of trees over the ranked alphabets and , respectively, and A is the domain of a semiring. The input and output product of with tree series ' : T ! A and : T ! A are the weighted tree transformations ' / and . , respectively, which are de ned by (' / )(t; u) = '(t) (t; u) and ( . )(t; u) = (t; u) (u) for every t 2 ...