Related papers: Parsing as Tree Traversal
More precise unification predictions require going beyond the lowest order, including 2-loop running of the couplings and a correct treatment of threshold effects. Here we revised two different approaches to deal with light thresholds,…
We introduce a unified generalization of several well-established high-throughput coding techniques including staircase codes, tiled diagonal zipper codes, continuously interleaved codes, open forward error correction (OFEC) codes, and…
Given a category with a bifunctor and natural isomorphisms for associativity, commutativity and left and right identity we do not assume that extra constraining diagrams hold. We introduce groupoids of coupling trees to describe a version…
We would like to congratulate Lee, Nadler and Wasserman on their contribution to clustering and data reduction methods for high $p$ and low $n$ situations. A composite of clustering and traditional principal components analysis, treelets is…
A transversal in a rooted tree is any set of nodes that meets every path from the root to a leaf. We let c(T,k) denote the number of transversals of size k in a rooted tree T. We define a partial order on the set of all rooted trees with n…
Generalized trees, we call them O-trees, are defined as hierarchical partial orders, i.e., such that the elements larger than any one are linearly ordered. Quasi-trees are, roughly speaking, undirected O-trees. For O-trees and quasi-trees,…
We construct a stationary random tree, embedded in the upper half plane, with prescribed offspring distribution and whose vertices are the atoms of a unit Poisson point process. This process which we call Hammersley's tree process extends…
The LR-drawing-method is a method of drawing an ordered rooted binary tree based on drawing one root-to-leaf path on a vertical line and attaching recursively obtained drawings of the subtrees on the left and right. In this paper, we study…
Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…
Graph encoders in AMR-to-text generation models often rely on neighborhood convolutions or global vertex attention. While these approaches apply to general graphs, AMRs may be amenable to encoders that target their tree-like structure. By…
When solving ill-posed inverse problems, one often desires to explore the space of potential solutions rather than be presented with a single plausible reconstruction. Valuable insights into these feasible solutions and their associated…
Graph classes of bounded tree rank were introduced recently in the context of the model checking problem for first-order logic of graphs. These graph classes are a common generalization of graph classes of bounded degree and bounded…
We introduce a new hierarchy of higher-order nested pushdown trees generalising Alur et al.'s concept of nested pushdown trees. Nested pushdown trees are useful representations of control flows in the verification of programs with recursive…
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
In this short paper, we explore a new way to refactor a simple but tricky-to-parallelize tree-traversal algorithm to harness multicore parallelism. Crucially, the refactoring draws from some classic techniques from programming-languages…
This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…
Our goal is to visualize an additional data dimension of a tree with multifaceted data through superimposition on vertical strips, which we call columns. Specifically, we extend upward drawings of unordered rooted trees where vertices have…
Parsing sentences into syntax trees can benefit downstream applications in NLP. Transition-based parsers build trees by executing actions in a state transition system. They are computationally efficient, and can leverage machine learning to…
Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees.…