Related papers: Letters, Colors, and Words: Constructing the Ideal…
Given a palette of six colors, a colored cube is a cube where each face is colored with exactly one color and each color appears on some face. Starting with an arbitrary collection of unit length colored cubes, one can try to arrange a…
We consider a puzzle such that a set of colored cubes is given as an instance. Each cube has unit length on each edge and its surface is colored so that what we call the Surface Color Condition is satisfied. Given a palette of six colors,…
In this paper, we consider block languages, namely sets of words having the same length, and we propose a new representation for these languages. In particular, given an alphabet of size $k$ and a length $\ell$, a block language can be…
This study presents a fascinating linguistic property related to the number of letters in words and their corresponding numerical values. By selecting any arbitrary word, counting its constituent letters, and subsequently spelling out the…
We tackle three optimization problems in which a colored graph, where each node is assigned a color, must be partitioned into colorful connected components. A component is defined as colorful if each color appears at most once. The problems…
A reconstruction problem of words from scattered factors asks for the minimal information, like multisets of scattered factors of a given length or the number of occurrences of scattered factors from a given set, necessary to uniquely…
English has a convoluted relationship between its pronunciation and spelling, which obscures its phonological structure for early literacy learners. This convoluted relationship has implications for early literacy software, particularly for…
Color-word associations play a fundamental role in human cognition and design applications. Large Language Models (LLMs) have become widely available and have demonstrated intelligent behaviors in various benchmarks with natural…
The problem of constructing optimal factoring automata arises in the context of unification factoring for the efficient execution of logic programs. Given an ordered set of $n$ strings of length $m$, the problem is to construct a trie-like…
We consider the problem of efficiently designing sets (codes) of equal-length DNA strings (words) that satisfy certain combinatorial constraints. This problem has numerous motivations including DNA computing and DNA self-assembly. Previous…
The 30 MacMahon colored cubes have each face painted with one of six colors and every color appears on at least one face. One puzzle involving these cubes is to create a $2\times2\times2$ model with eight distinct MacMahon cubes to recreate…
This paper studies problems related to visibility among points in the plane. A point $x$ \emph{blocks} two points $v$ and $w$ if $x$ is in the interior of the line segment $\bar{vw}$. A set of points $P$ is \emph{$k$-blocked} if each point…
In some areas of computing, natural language processing and information science, progress is made by sharing datasets and challenging the community to design the best algorithm for an associated task. This article introduces a shared…
General purpose language models (LMs) encounter difficulties when processing domain-specific jargon and terminology, which are frequently utilized in specialized fields such as medicine or industrial settings. Moreover, they often find it…
Color names are often made up of multiple words. As a task in natural language understanding we investigate in depth the capacity of neural networks based on sums of word embeddings (SOWE), recurrence (LSTM and GRU based RNNs) and…
We introduce the task of algorithm class prediction for programming word problems. A programming word problem is a problem written in natural language, which can be solved using an algorithm or a program. We define classes of various…
In the Colored Bin Packing problem a set of items with varying weights and colors must be packed into bins of uniform weight limit such that no two items of the same color may be packed adjacently within a bin. We solve this problem for the…
We revisit a classical crossword filling puzzle which already appeared in Garey\&Jonhson's book. We are given a grid with $n$ vertical and horizontal slots and a dictionary with $m$ words and are asked to place words from the dictionary in…
Motivated by the study of genome rearrangements, the NP-hard Minimum Common String Partition problems asks, given two strings, to split both strings into an identical set of blocks. We consider an extension of this problem to unbalanced…
We address the problem of constructing a fast lossless code in the case when the source alphabet is large. The main idea of the new scheme may be described as follows. We group letters with small probabilities in subsets (acting as super…