Related papers: Letters, Colors, and Words: Constructing the Ideal…
Graph coloring is a computationally difficult problem, and currently the best known classical algorithm for $k$-coloring of graphs on $n$ vertices has runtimes $\Omega(2^n)$ for $k\ge 5$. The list coloring problem asks the following more…
We present an iterative procedure to build a Chinese language model (LM). We segment Chinese text into words based on a word-based Chinese language model. However, the construction of a Chinese LM itself requires word boundaries. To get out…
Given a word $w$, what is the maximum possible number of appearances of $w$ reading contiguously along any of the directions in $\{-1, 0, 1\}^d \setminus \{\mathbf{0}\}$ in a large $d$-dimensional grid (as in a word search)? Patchell and…
Lowering the barriers to computer programming requires understanding how to scaffold learning. Parsons problems, which require learners to drag-and-drop blocks of code into the correct order and indentation, are proving to be beneficial for…
Information is often encoded as an aperiodic chain of building blocks. Modern digital computers use bits as the building blocks, but in general the choice of building blocks depends on the nature of the information to be encoded. What are…
By the Road Coloring Theorem (Trahtman, 2008), the edges of any aperiodic directed multigraph with a constant out-degree can be colored such that the resulting automaton admits a reset word. There may also be a need for a particular reset…
Deep learning networks find intricate features in large datasets using the backpropagation algorithm. This algorithm repeatedly adjusts the network connections.' weights and examining the "hidden" nodes behavior between the input and output…
Crosswords are a form of word puzzle that require a solver to demonstrate a high degree of proficiency in natural language understanding, wordplay, reasoning, and world knowledge, along with adherence to character and length constraints. In…
This paper focuses on exact approaches for the Colored Bin Packing Problem (CBPP), a generalization of the classical one-dimensional Bin Packing Problem in which each item has, in addition to its length, a color, and no two items of the…
In this paper, we consider the problem of constructing optimal average-length binary codes under the constraint that each codeword must contain at most $D$ ones, where $D$ is a given input parameter. We provide an $O(n^2D)$-time complexity…
We provide geometric methods and algorithms to verify, construct and enumerate pairs of words (of specified length over a fixed $m$-letter alphabet) that form identities in the semigroup $\ut{n}$ of $n\times n$ upper triangular tropical…
In natural speech, the speaker does not pause between words, yet a human listener somehow perceives this continuous stream of phonemes as a series of distinct words. The detection of boundaries between spoken words is an instance of a…
We study regular expressions that use variables, or parameters, which are interpreted as alphabet letters. We consider two classes of languages denoted by such expressions: under the possibility semantics, a word belongs to the language if…
Code-mixing, the practice of switching between languages within a conversation, poses unique challenges for traditional NLP. Existing benchmarks are limited by their narrow language pairs and tasks, failing to adequately assess large…
In the Edge Coloring problem, we are given an undirected graph $G$ with $n$ vertices and $m$ edges, and are tasked with finding the smallest positive integer $k$ so that the edges of $G$ can be assigned $k$ colors in such a way that no two…
Wordle, a word guessing game rose to global popularity in the January of 2022. The goal of the game is to guess a five-letter English word within six tries. Each try provides the player with hints by means of colour changing tiles which…
Dense word embeddings, which encode semantic meanings of words to low dimensional vector spaces have become very popular in natural language processing (NLP) research due to their state-of-the-art performances in many NLP tasks. Word…
Automatic generation of natural language from images has attracted extensive attention. In this paper, we take one step further to investigate generation of poetic language (with multiple lines) to an image for automatic poetry creation.…
We describe a general technique for obtaining provably correct, non-blocking implementations of a large class of tree data structures where pointers are directed from parents to children. Updates are permitted to modify any contiguous…
This research presents ORUGA, a method that tries to automatically optimize the readability of any text in English. The core idea behind the method is that certain factors affect the readability of a text, some of which are quantifiable…