相关论文: Exponentially Huge Natural Deduction proofs are Re…

This article precisely defines huge proofs within the system of Natural Deduction for the Minimal implicational propositional logic \mil. This is what we call an unlimited family of super-polynomial proofs. We consider huge families of…

We study the asymptotic number of certain monotonically labeled increasing trees arising from a generalized evolution process. The main difference between the presented model and the classical model of binary increasing trees is that the…

Decision trees have long been recognized as models of choice in sensitive applications where interpretability is of paramount importance. In this paper, we examine the computational ability of Boolean decision trees in deriving, minimizing,…

Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…

We give a representation for labeled ordered trees that supports labeled queries such as finding the i-th ancestor of a node with a given label. Our representation is succinct, namely the redundancy is small-o of the optimal space for…

In this work we introduce and study various generalizations of the notion of increasingly labelled trees, where the label of a child node is always larger than the label of its parent node, to multilabelled tree families, where the nodes in…

This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…

Distributed proofs are mechanisms enabling the nodes of a network to collectivity and efficiently check the correctness of Boolean predicates on the structure of the network, or on data-structures distributed over the nodes (e.g., spanning…

We analyse a maximum-likelihood approach for combining phylogenetic trees into a larger `supertree'. This is based on a simple exponential model of phylogenetic error, which ensures that ML supertrees have a simple combinatorial description…

Boosted trees is a dominant ML model, exhibiting high accuracy. However, boosted trees are hardly intelligible, and this is a problem whenever they are used in safety-critical applications. Indeed, in such a context, rigorous explanations…

We investigate the number of permutations that occur in random labellings of trees. This is a generalisation of the number of subpermutations occurring in a random permutation. It also generalises some recent results on the number of…

We investigate the statistics of trees grown from some initial tree by attaching links to preexisting vertices, with attachment probabilities depending only on the valence of these vertices. We consider the asymptotic mass distribution that…

Exponential growth occurs when the growth rate of a given quantity is proportional to the quantity's current value. Surprisingly, when exponential growth data is plotted as a simple histogram disregarding the time dimension, a remarkable…

We study fragmentation of a random recursive tree into a forest by repeated removal of nodes. The initial tree consists of N nodes and it is generated by sequential addition of nodes with each new node attaching to a randomly-selected…

The metric dimension of a graph $G$ is the minimal size of a subset $R$ of vertices of $G$ that, upon reporting their graph distance from a distingished (source) vertex $v^\star$, enable unique identification of the source vertex $v^\star$…

Inferring a decision tree from a given dataset is one of the classic problems in machine learning. This problem consists of buildings, from a labelled dataset, a tree such that each node corresponds to a class and a path between the tree…

It is well-known that the size of propositional classical proofs can be huge. Proof theoretical studies discovered exponential gaps between normal or cut free proofs and their respective non-normal proofs. The aim of this work is to study…

Given two messages - as linear sequences of letters, it is immediate to determine whether one can be transformed into the other by simple substitution cipher of the letters. On the other hand, if the letters are carried as labels on nodes…

A random forest prediction can be computed by the scalar product of the labels of the training examples and a set of weights that are determined by the leafs of the forest into which the test object falls; each prediction can hence be…

We consider the counting problem of the number of \textit{leaf-labeled increasing trees}, where internal nodes may have an arbitrary number of descendants. The set of all such trees is a discrete representation of the genealogies obtained…