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Tandem duplication in DNA is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain {\em et al.} (2016) proposed the study of codes that…
An optimal algorithm is presented about Conflict-Free Coloring for connected subgraphs of tree of rings. Suppose the number of the rings in the tree is |T| and the maximum length of rings is |R|. A presented algorithm in [1] for a Tree of…
The use of children's drawings to examining their conceptual understanding has been proven to be an effective method, but there are two major problems with previous research: 1. The content of the drawings heavily relies on the task, and…
The iterated learning model simulates the transmission of language from generation to generation in order to explore how the constraints imposed by language transmission facilitate the emergence of language structure. Despite each modelled…
The past few years has seen the application of machine learning utilised in the exploration of new materials. As in many fields of research - the vast majority of knowledge is published as text, which poses challenges in either a…
Finding all the words on a Boggle board is a classic computer programming problem. With a fast Boggle solver, local optimization techniques such as hillclimbing and simulated annealing can be used to find particularly high-scoring boards.…
Across languages, numeral systems vary widely in how they construct and combine numbers. While humans consistently learn to navigate this diversity, large language models (LLMs) struggle with linguistic-mathematical puzzles involving…
An edge-colored graph $G$ is said to be rainbow connected if between each pair of vertices there exists a path which uses each color at most once. The rainbow connection number, denoted by $rc(G)$, is the minimum number of colors needed to…
Block codes are considered for improving the reliability of messages stored in a computer memory with both stuck-at defects and random errors. It is assumed that the side information about the state of the defects is available to the…
The paper considers the NP-hard graph vertex coloring problem, which differs from traditional problems in which it is required to color vertices with a given (or minimal) number of colors so that adjacent vertices have different colors. In…
The avalanche quantity of the information developed by mankind has led to concept of automation of knowledge extraction - Data Mining ([1]). This direction is connected with a wide spectrum of problems - from recognition of the fuzzy set to…
Existing reasoning benchmarks for large language models (LLMs) frequently fail to capture authentic creativity, often rewarding memorization of previously observed patterns. We address this shortcoming with Sudoku-Bench, a curated benchmark…
Stickers, though small, are a highly condensed form of visual expression, ubiquitous across messaging platforms and embraced by diverse cultures, genders, and age groups. Despite their popularity, sticker retrieval remains an underexplored…
The use of language models for generating lyrics and poetry has received an increased interest in the last few years. They pose a unique challenge relative to standard natural language problems, as their ultimate purpose is reative, notions…
Algorithms are the engine for reproducible problem-solving. We present a framework automating algorithm discovery by conceptualizing them as sequences of operations, represented as tokens. These computational tokens are chained using a…
Large language models (LLMs) are deployed on increasingly complex tasks that require multi-step decision-making. Understanding their algorithmic reasoning abilities is therefore crucial. However, we lack a diagnostic benchmark for…
In this paper, we consider the problem of identifying patterns of interest in colored strings. A colored string is a string where each position is assigned one of a finite set of colors. Our task is to find substrings of the colored string…
Large language models (LLMs), such as GPT-3 and GPT-4, have demonstrated exceptional performance in various natural language processing tasks and have shown the ability to solve certain reasoning problems. However, their reasoning…
Programming often involves converting detailed and complex specifications into code, a process during which developers typically utilize visual aids to more effectively convey concepts. While recent developments in Large Multimodal Models…
Large Language Models (LLMs) have achieved human-level proficiency across diverse tasks, but their ability to perform rigorous mathematical problem solving remains an open challenge. In this work, we investigate a fundamental yet…