Related papers: Trees in Partial Higher Dimensional Automata
Data trees serve as an abstraction of structured data, such as XML documents. A number of specification formalisms for languages of data trees have been developed, many of them adhering to the paradigm of register automata, which is based…
This paper introduces a novel supervised classification strategy that integrates functional data analysis (FDA) with tree-based methods, addressing the challenges of high-dimensional data and enhancing the classification performance of…
In this article, we propose a method to design loss functions based on component trees which can be optimized by gradient descent algorithms and which are therefore usable in conjunction with recent machine learning approaches such as…
We present a new approach to the following meta-problem: given a quantitative property of trees, design a type system such that the desired property for the tree generated by an infinitary ground lambda-term corresponds to some property of…
Staged trees are probabilistic graphical models capable of representing any class of non-symmetric independence via a coloring of its vertices. Several structural learning routines have been defined and implemented to learn staged trees…
Tree sets are posets with additional structure that generalize tree-like objects in graphs, matroids, or other combinatorial structures. They are a special class of abstract separation systems. We study infinite tree sets and how they…
To most mathematicians and computer scientists the word ``tree'' conjures up, in addition to the usual image, the image of a connected graph with no circuits. In the last few years various types of trees have been the subject of much…
It is well known that for a regular tree language it is decidable whether or not it can be recognized by a deterministic top-down tree automaton (DTA). However, the computational complexity of this problem has not been studied. We show that…
One of the main virtues of trees is to represent formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differential equations and functional (Lagrange) inversion in…
The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed for binary tree spaces. In this study, we extend these ideas…
The metric space of phylogenetic trees defined by Billera, Holmes, and Vogtmann, which we refer to as BHV space, provides a natural geometric setting for describing collections of trees on the same set of taxa. However, it is sometimes…
A deterministic finite automaton in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. We characterize such automata in terms of graphs…
Non-well-founded trees are used in mathematics and computer science, for modelling non-well-founded sets, as well as non-terminating processes or infinite data-structures. Categorically, they arise as final coalgebras for polynomial…
Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…
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…
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…
The HOM problem, which asks whether the image of a regular tree language under a given tree homomorphism is again regular, is known to be decidable [Godoy & Gim\'enez: The HOM problem is decidable. JACM 60(4), 2013]. However, the problem…
Networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes. A tree is characterized by two parameters: its ramification and its depth. The local dynamics at the…
Automata learning is a popular technique used to automatically construct an automaton model from queries. Much research went into devising ad hoc adaptations of algorithms for different types of automata. The CALF project seeks to unify…
We introduce tree stack automata as a new class of automata with storage and identify a restricted form of tree stack automata that recognises exactly the multiple context-free languages.