Related papers: Hat Puzzles
This article contains a selection of problems from the American Mathematics Competitions.
Based on Lyndon words, a new Sudoku-like puzzle is presented and some relative theoretical questions are proposed.
I will give a new way to understand the Geometric Langlands Program.
The paper announces the new long-term challenge for improving the performance of automatic speech recognition systems. The goal of the challenge is to investigate methods of correcting the recognition results on the basis of previously made…
Answer set programming is a prominent declarative programming paradigm used in formulating combinatorial search problems and implementing different knowledge representation formalisms. Frequently, several related and yet substantially…
The purpose of this short note is to show the interplay between math outreach and conducting original research, in particular how each can build off the other.
These notes give a statement of the "fundamental lemma," which is a conjectural identity between p-adic integrals that arises as part of the Langlands program.
We establish fun parallels between coin-weighing puzzles and knights-and-knaves puzzles.
In a previous paper (q-alg/9501022) we suggested some algorithms that could be useful in solving the problem of knot classification. Here we continue this discussion by answering questions raised in that paper and by commenting on practical…
The idea of writing a table of probabilistic data for a quantum or classical system, and of decomposing this table in a compact way, leads to a shortcut for Hardy's formalism, and gives new perspectives on foundational issues.
This is an update of my problem list.
Humor is an important social phenomenon, serving complex social and psychological functions. However, despite being studied for millennia humor is computationally not well understood, often considered an AI-complete problem. In this work,…
In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear…
Solving crossword puzzles requires diverse reasoning capabilities, access to a vast amount of knowledge about language and the world, and the ability to satisfy the constraints imposed by the structure of the puzzle. In this work, we…
This short paper describes a simple and intuitive Prolog program, a metainterpreter, that computes the bottom up meaning of a simple positive Horn clause definition. It involves a simple transformation of the object program rules into…
Over the years, integer linear programs have been employed to model inference in many natural language processing problems. This survey is meant to guide the reader through the process of framing a new inference problem as an instance of an…
In this paper, we consider the problem of lifted inference in the context of Prism-like probabilistic logic programming languages. Traditional inference in such languages involves the construction of an explanation graph for the query and…
The rapid adoption of Generative AI, including LLM-based chatbots like ChatGPT, has highlighted the need for accessible ways to support public understanding and AI literacy. To address this need, we introduce a game-based, interactive…
We present a new technique (called pennants) for displaying the descriptors related to a descriptor across literatures, rather in a thesaurus. It has definite implications for online searching and browsing. Pennants, named for the flag they…
We discuss further around the generalized Langlands Program, by using $\infty$-categoricalization and $\infty$-analytic stackification.