相关论文: Hardness of Mastermind

We recast move generators for solving board games as operations on compressed sets of strings. We aim for compressed representations with space sublinear in the number of game positions for interesting sets of positions, move generation in…

How can we predict the difficulty of a Sudoku puzzle? We give an overview of difficulty rating metrics and evaluate them on extensive dataset on human problem solving (more then 1700 Sudoku puzzles, hundreds of solvers). The best results…

Reinforcement learning has recently been used to approach well-known NP-hard combinatorial problems in graph theory. Among these problems, Hamiltonian cycle problems are exceptionally difficult to analyze, even when restricted to individual…

Although board games and video games have been studied for decades in artificial intelligence research, challenging word games remain relatively unexplored. Word games are not as constrained as games like chess or poker. Instead, word game…

Spatial puzzles composed of rigid objects, flexible strings and holes offer interesting domains for reasoning about spatial entities that are common in the human daily-life's activities. The goal of this work is to investigate the automated…

We introduce Pencil Puzzle Bench, a framework for evaluating large language model reasoning through pencil puzzles, a family of constraint-satisfaction problems closely related to NP-complete problems, with deterministic, step-level…

The problem we are considering is the following. A colorblind player is given a set $B = \{b_1,b_2,...,b_N\}$ of $N$ colored balls. He knows that each ball is colored either red or green, and that there are less green balls (this will be…

The classical Maker-Breaker positional game is played on a board which is a hypergraph $\mathcal{H}$, with two players, Maker and Breaker, alternately claiming vertices of $\mathcal{H}$ until all the vertices are claimed. When the game…

A popular computer puzzle, the game of Minesweeper requires its human players to have a mix of both luck and strategy to succeed. Analyzing these aspects more formally, in our research we assessed the feasibility of a novel methodology…

In this paper, we give simple NP-hardness reductions for three popular video games. The first is Baba Is You, an award winning 2D block puzzle game with the key premise being the ability to rewrite the rules of the game. The second is Fez,…

Pebble games were extensively studied in the 1970s and 1980s in a number of different contexts. The last decade has seen a revival of interest in pebble games coming from the field of proof complexity. Pebbling has proven to be a useful…

In bilevel optimization problems, a leader and a follower make their decisions in a hierarchy, and both decisions may influence each other. Usually one assumes that both players have full knowledge also of the other player's data. In a more…

Various forms of sorting problems have been studied over the years. Recently, two kinds of sorting puzzle apps are popularized. In these puzzles, we are given a set of bins filled with colored units, balls or water, and some empty bins.…

In the ordinal Matroid Secretary Problem (MSP), elements from a weighted matroid are presented in random order to an algorithm that must incrementally select a large weight independent set. However, the algorithm can only compare pairs of…

As large language models (LLMs) are increasingly deployed across diverse domains, ensuring their safety has become a critical concern. In response, studies on jailbreak attacks have been actively growing. Existing approaches typically rely…

We introduce and study a novel generalization of the classical Knapsack Problem (KP), called the Colored Knapsack Problem (CKP). In this problem, the items are partitioned into classes of colors and the packed items need to be ordered such…

The problem of CSP sparsification asks: for a given CSP instance, what is the sparsest possible reweighting such that for every possible assignment to the instance, the number of satisfied constraints is preserved up to a factor of $1 \pm…

Tumbleweed is a popular two-player perfect-information new territorial game played at the prestigious Mind Sport Olympiad. We define a generalized version of the game, where the board size is arbitrary and so is the possible number of…

We study the problem of computing an $\epsilon$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players…

This paper presents iNNK, a multiplayer drawing game where human players team up against an NN. The players need to successfully communicate a secret code word to each other through drawings, without being deciphered by the NN. With this…