Related papers: Pr\"ufer codes for hypertrees
We study the new problem of Huffman-like codes subject to individual restrictions on the code-word lengths of a subset of the source words. These are prefix codes with minimal expected code-word length for a random source where additionally…
We divide the class of infinite computable trees into three types. For the first and second types, $0'$ computes a nontrivial self-embedding while for the third type $0''$ computes a nontrivial self-embedding. These results are optimal and…
In this paper, we introduce an achievability bound on the frame error rate of random tree code ensembles under a sequential decoding algorithm with a hard computational limit and consider the optimization of the random tree code ensembles…
The depth-bounded fragment of the pi-calculus is an expressive class of systems enjoying decidability of some important verification problems. Unfortunately membership of the fragment is undecidable. We propose a novel type system,…
A general class of the almost instantaneous fixed-to-variable-length (AIFV) codes is proposed, which contains every possible binary code we can make when allowing finite bits of decoding delay. The contribution of the paper lies in the…
This article presents two novel algorithms for generating random increasing trees. The first algorithm efficiently generates strictly increasing binary trees using an ad hoc method. The second algorithm improves the recursive method for…
We introduce \emph{Term Coding}, a novel framework for analysing extremal problems in discrete mathematics by encoding them as finite systems of \emph{term equations} (and, optionally, \emph{non-equality constraints}). In its basic form,…
We give an algorithm for computing the Teichm\"uller polynomial for a certain class of fibered alternating links associated to trees. Furthermore, we exhibit a mutant pair of such links distinguished by the Teichm\"uller polynomial.
Logical frameworks are successful in modeling proof systems. Recently, CoLF extended the logical framework LF to support higher-order rational terms that enable adequate encoding of circular objects and derivations. In this paper, we…
Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward…
We obtain a closed-form expression for the Wiener index of binomial trees. We outline efficient algorithms for computing the Wiener indices of Fibonacci and binary Fibonacci trees.
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…
We provide an expository account of some of the Hopf algebras that can be defined using trees, labeled trees, ordered trees and heap ordered trees. We also describe some actions of these Hopf algebras on algebra of functions.
We look for partition theorems for large subtrees for suitable uncountable trees and colourings. We concentrate on sub-trees of $^{\kappa \ge} 2$ expanded by a well ordering of each level. Unlike earlier works, we do not ask the embedding…
We prove an accessibility theorem for finite-index splittings of groups. Given a finitely presented group G there is a number n(G) such that, for every reduced locally finite G-tree T with finitely generated stabilizers, T/G has at most…
We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are described up to isomorphism.
We propose almost instantaneous fixed-to-variable-length (AIFV) codes such that two (resp. $K-1$) code trees are used if code symbols are binary (resp. $K$-ary for $K \geq 3$), and source symbols are assigned to incomplete internal nodes in…
Recent efforts to learn reward functions from human feedback have tended to use deep neural networks, whose lack of transparency hampers our ability to explain agent behaviour or verify alignment. We explore the merits of learning…
New bounds on the cardinality of permutation codes equipped with the Ulam distance are presented. First, an integer-programming upper bound is derived, which improves on the Singleton-type upper bound in the literature for some lengths.…
We present a self-training approach to unsupervised dependency parsing that reuses existing supervised and unsupervised parsing algorithms. Our approach, called `iterated reranking' (IR), starts with dependency trees generated by an…