Related papers: More restricted growth functions: Gray codes and e…
Despite recent advances, goal-directed generation of structured discrete data remains challenging. For problems such as program synthesis (generating source code) and materials design (generating molecules), finding examples which satisfy…
This paper proposes a generic formulation that significantly expedites the training and deployment of image classification models, particularly under the scenarios of many image categories and high feature dimensions. As a defining…
Let $A_q(n,d)$ be the maximum order (maximum number of codewords) of a $q$-ary code of length $n$ and Hamming distance at least $d$. And let $A(n,d,w)$ that of a binary code of constant weight $w$. Building on results from algebraic graph…
Unary coding is useful but it is redundant in its standard form. Unary coding can also be seen as spatial coding where the value of the number is determined by its place in an array. Motivated by biological finding that several neurons in…
Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…
We provide a trace partitioned Gray code for the set of q-ary strings avoiding a pattern constituted by k consecutive equal symbols. The definition of this Gray code is based on two different constructions, according to the parity of q.…
Constrained codes are used to prevent errors from occurring in various data storage and data transmission systems. They can help in increasing the storage density of magnetic storage devices, in managing the lifetime of electronic storage…
Robust Gray codes were introduced by (Lolck and Pagh, SODA 2024). Informally, a robust Gray code is a (binary) Gray code $\mathcal{G}$ so that, given a noisy version of the encoding $\mathcal{G}(j)$ of an integer $j$, one can recover…
In most constraint programming systems, a limited number of search engines is offered while the programming of user-customized search algorithms requires low-level efforts, which complicates the deployment of such algorithms. To alleviate…
Large Language Models (LLMs) have demonstrated great promise in generating code, especially when used inside an evolutionary computation framework to iteratively optimize the generated algorithms. However, in some cases they fail to…
Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics (the study of evolutionary trees and networks). Although these networks have a number of attractive mathematical…
We study the bounded regions in a generic slice of the hyperplane arrangement in $\mathbb{R}^n$ consisting of the hyperplanes defined by $x_i$ and $x_i+x_j$. The bounded regions are in bijection with several classes of combinatorial…
In this paper, we consider situations in which a given logical function is realized by a multithreshold threshold function. In such situations, constant functions can be easily obtained from multithreshold threshold functions, and…
The restricted Boltzmann machine (RBM) is a representative generative model based on the concept of statistical mechanics. In spite of the strong merit of interpretability, unavailability of backpropagation makes it less competitive than…
An equitable graph coloring is a proper vertex coloring of a graph G where the sizes of the color classes differ by at most one. The equitable chromatic number is the smallest number k such that G admits such equitable k-coloring. We focus…
Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…
Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…
We define a Johnson graph code as a subspace of labelings of the vertices in a Johnson graph with the property that labelings are uniquely determined by their restriction to vertex neighborhoods specified by the parameters of the code. We…
We begin a systematic study of the enumerative combinatorics of mixed succession rules, which are succession rules such that, in the associated generating tree, the nodes are allowed to produce their sons at several different levels…
First-order model counting (FOMC) is a computational problem that asks to count the models of a sentence in finite-domain first-order logic. In this paper, we argue that the capabilities of FOMC algorithms to date are limited by their…