Related papers: Two or three things I know about tree transducers
This paper investigates the execution of tree-shaped task graphs using multiple processors. Each edge of such a tree represents a large IO file. A task can only be executed if all input and output files fit into memory, and a file can only…
It is well known that for a given bottom-up tree automaton it can be decided whether or not there exists deterministic top-down tree automaton that recognized the same tree language. Recently it was claimed that such a decision can be…
We present graph-based translation models which translate source graphs into target strings. Source graphs are constructed from dependency trees with extra links so that non-syntactic phrases are connected. Inspired by phrase-based models,…
Random forests are decision tree ensembles that can be used to solve a variety of machine learning problems. However, as the number of trees and their individual size can be large, their decision making process is often incomprehensible. In…
A word-to-word function is rational if it can be realized by a non-deterministic one-way transducer. Over finite words, it is a classical result that any rational function is regular, i.e. it can be computed by a deterministic two-way…
Let $T$ be a weighted tree. The weight of a subtree $T_1$ of $T$ is defined as the product of weights of vertices and edges of $T_1$. We obtain a linear-time algorithm to count the sum of weights of subtrees of $T$. As applications, we…
We investigate the structure of connected graphs, not necessarily locally finite, with infinitely many ends. On the one hand we study end-transitive such graphs and on the other hand we study such graphs with the property that the…
This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…
We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…
Transformers have demonstrated remarkable capabilities in multi-step reasoning tasks. However, understandings of the underlying mechanisms by which they acquire these abilities through training remain limited, particularly from a…
While the successes of transformers across many domains are indisputable, accurate understanding of the learning mechanics is still largely lacking. Their capabilities have been probed on benchmarks which include a variety of structured and…
Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…
Trees are partial orders in which every element has a linearly ordered set of predecessors. Here we initiate the exploration of the structural theory of trees with the study of different notions of \emph{branching in trees} and of…
Levy-Longo Trees and Bohm Trees are the best known tree structures on the {\lambda}-calculus. We give general conditions under which an encoding of the {\lambda}-calculus into the {\pi}-calculus is sound and complete with respect to such…
In this paper, we study the induced homological sequence and the induced merge tree of a discrete Morse function on a tree. A discrete Morse function on a tree gives rise to a sequence of Betti numbers that keep track of the number of…
Transition-based top-down parsing with pointer networks has achieved state-of-the-art results in multiple parsing tasks, while having a linear time complexity. However, the decoder of these parsers has a sequential structure, which does not…
This paper grew out of three tutorial lectures on automatic structures given by the first author at the Logic Colloquium 2007. We discuss variants of automatic structures related to several models of computation: word automata, tree…
We study trees where each successor set is equipped with some additional structure. We introduce a family of automaton models for such trees and prove their equivalence to certain fixed-point logics. As a consequence we obtain…
This paper describes a data-driven framework to parse musical sequences into dependency trees, which are hierarchical structures used in music cognition research and music analysis. The parsing involves two steps. First, the input sequence…
Hidden tree Markov models allow learning distributions for tree structured data while being interpretable as nondeterministic automata. We provide a concise summary of the main approaches in literature, focusing in particular on the…