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In this paper we argue that Massively Multiplayer Online Games (MMOGs), also known as Large Games are an interesting research tool for policy experimentation. One of the major problems with lawmaking is that testing the laws is a difficult…
The Connections puzzle is a word association game published daily by The New York Times (NYT). In this game, players are asked to find groups of four words that are connected by a common theme. While solving a given Connections puzzle…
Wordle is a single-player word-guessing game where the goal is to discover a secret word $w$ that has been chosen from a dictionary $D$. In order to discover $w$, the player can make at most $\ell$ guesses, which must also be words from…
Large language models (LLMs) have achieved striking successes on many benchmarks, yet recent studies continue to expose fundamental weaknesses. In this paper, we introduce Concept, a simple word-guessing board game, as a benchmark for…
Reasoning is a fundamental capability of large language models (LLMs), enabling them to comprehend, analyze, and solve complex problems. In this paper, we introduce TextGames, an innovative benchmark specifically crafted to assess LLMs…
We show that human players' gameplay in the game of Wordle is influenced by the semantics, orthography, and phonology of the player's previous guesses. We compare actual human players' guesses with near-optimal guesses using NLP techniques.…
Logic programming with fixed-point definitions is a useful extension of traditional logic programming. Fixed-point definitions can capture simple model checking problems and closed-world assumptions. Its operational semantics is typically…
A major challenge in inductive logic programming is learning big rules. To address this challenge, we introduce an approach where we join small rules to learn big rules. We implement our approach in a constraint-driven system and use…
Logic reasoning is a significant ability of human intelligence and also an important task in artificial intelligence. The existing logic reasoning methods, quite often, need to design some reasoning patterns beforehand. This has led to an…
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…
A model checking computation checks whether a given logical sentence is true in a given finite structure. Provenance analysis abstracts from such a computation mathematical information on how the result depends on the atomic data that…
Differential game logic (dGL) is a logic for specifying and verifying properties of hybrid games, i.e. games that combine discrete, continuous, and adversarial dynamics. Unlike hybrid systems, hybrid games allow choices in the system…
I discuss puzzles that require thinking outside the box. I also discuss the box inside of which many people think.
While previous researchers have performed an exhaustive search to determine an optimal Wordle strategy, that computation is very time consuming and produced a strategy using words that are unfamiliar to most people. With Wordle solutions…
Consider a periodical (in two independent directions) tiling of the plane with polygons (faces). In this article we shall only give examples using squares, regular hexagons, equilateral triangles and parallelograms ("unions" of two…
Sumplete is a logic puzzle famous for being developed by ChatGPT. The puzzle consists of a rectangular grid, with each cell containing a number. The player has to cross out some numbers such that the sum of uncrossed numbers in each row and…
In this work, we have designed and implemented, based on traditional board games such as the game of the Goose or Parchis, an educational software that aim to reinforce the learning of children. The idea that we are going to develop to do…
In this paper we give a mathematical model for a game that we call picture cube puzzle and investigate its properties. The central question is the number of moves required to solve the puzzle. A mathematical discussion is followed by the…
Children learn though play. We introduce the analogous idea of learning programs through play. In this approach, a program induction system (the learner) is given a set of tasks and initial background knowledge. Before solving the tasks,…
For any odd integer $n\geq3$ a board (of size $n$) is a square array of $n\times n$ positions with a simple rule of how to move between positions. The goal of the game we introduce is to find a path from the upper left corner of a board to…