Related papers: Hat Puzzles
Large language models (LLMs), including ChatGPT, Bard, and Llama, have achieved remarkable successes over the last two years in a range of different applications. In spite of these successes, there exist concerns that limit the wide…
The purpose of this paper is to describe and elaborate the philosophical ideas behind hyperstructures and structure formation in general and emphasize the key ideas of the Hyperstructure Program.
Cross-coverage of a program P refers to the test coverage measured over a different program Q that is functionally equivalent to P. The novel concept of cross-coverage can find useful applications in the test of redundant software. We apply…
Traditional language models face a challenge from hallucinations. Their very presence casts a large, dangerous shadow over the promising realm of natural language processing. It becomes crucial to understand the various kinds of…
Large Language Models (LLMs) have transformed the Natural Language Processing (NLP) landscape with their remarkable ability to understand and generate human-like text. However, these models are prone to ``hallucinations'' -- outputs that do…
Large Language Models (LLMs) have upended decades of pedagogy in computing education. Students previously learned to code through \textit{writing} many small problems with less emphasis on code reading and comprehension. Recent research has…
This expository paper discusses some conjectures related to visibility and blockers for sets of points in the plane.
In this paper, we describe a novel architecture which can generate hilarious captions for a given input image. The architecture is split into two halves, i.e. image captioning and hilarious text conversion. The architecture starts with a…
We present a system capable of automatically solving combinatorial logic puzzles given in (simplified) English. It involves translating the English descriptions of the puzzles into answer set programming(ASP) and using ASP solvers to…
Inductive logic programming (ILP) is a form of logic-based machine learning. The goal is to induce a hypothesis (a logic program) that generalises given training examples. As ILP turns 30, we review the last decade of research. We focus on…
The present paper aims to survey known results and to point out the wealth of rather important open problems that are out there.
Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find…
We discuss ``puzzles of prisoners and hats`` with infinitely many prisoners and more than two hat colors. Assuming that the set of hat colors is equipped with a commutative group structure, we prove strategic equivalence among puzzles of…
We propose a new formal language for the expressive representation of probabilistic knowledge based on Answer Set Programming (ASP). It allows for the annotation of first-order formulas as well as ASP rules and facts with probabilities and…
We investigate the use of Answer Set Programming to solve variations of gossip problems, by modeling them as epistemic planning problems.
In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory. This scientific…
Prompting and fine-tuning have emerged as two competing paradigms for augmenting language models with new capabilities, such as the use of tools. Prompting approaches are quick to set up but rely on providing explicit demonstrations of each…
The aim of these notes is to give an overview of several aspects of what has come to be called the relative Langlands program, a theme that takes its origin in the study of automorphic periods and their relations to particular cases of…
This note concerns a search for publications in which one can find statements that explain the concept of an operating system, reasons for introducing operating systems, a formalization of the concept of an operating system or theory about…
We investigate the complexity of a puzzle that turns out to be NL-complete.