相关论文: Hardness of Mastermind

Estimating the performance difficulty of a musical score is crucial in music education for adequately designing the learning curriculum of the students. Although the Music Information Retrieval community has recently shown interest in this…

Muller games are played by two players moving a token along a graph; the winner is determined by the set of vertices that occur infinitely often. The central algorithmic problem is to compute the winning regions for the players. Different…

Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…

The Matroid Secretary Problem (MSP) is one of the most prominent settings for online resource allocation and optimal stopping. A decision-maker is presented with a ground set of elements $E$ revealed sequentially and in random order. Upon…

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…

Arithmetic puzzle games provide a controlled setting for studying difficulty in mathematical reasoning tasks, a core challenge in adaptive learning systems. We investigate the structural determinants of difficulty in a class of integer…

Security questions are one of the techniques used to recover passwords. The main limitation of security questions is that users find strong answers difficult to remember. This leads users to trade-off security for the convenience of an…

In this paper, we show that the problem of determining whether one player can force a win in a multiplayer version of the children's card game War is PSPACE-hard. The same reduction shows that a related problem, asking whether a player can…

We study the complexity of a particular class of board games, which we call `slide and merge' games. Namely, we consider 2048 and Threes, which are among the most popular games of their type. In both games, the player is required to slide…

We prove the computational intractability of rotating and placing $n$ square tiles into a $1 \times n$ array such that adjacent tiles are compatible--either equal edge colors, as in edge-matching puzzles, or matching tab/pocket shapes, as…

Braid is a 2008 puzzle game centered around the ability to reverse time. We show that Braid can simulate an arbitrary computation. Our construction makes no use of Braid's unique time mechanics, and therefore may apply to many other video…

Poker is ideal for testing automated reasoning under uncertainty. It introduces uncertainty both by physical randomization and by incomplete information about opponents hands.Another source OF uncertainty IS the limited information…

The Sudoku puzzle has achieved worldwide popularity recently, and attracted great attention of the computational intelligence community. Sudoku is always considered as Satisfiability Problem or Constraint Satisfaction Problem. In this…

Mirror games were invented by Garg and Schnieder (ITCS 2019). Alice and Bob take turns (with Alice playing first) in declaring numbers from the set {1,2, ...2n}. If a player picks a number that was previously played, that player loses and…

We study the computational complexity of an important property of simple, regular and weighted games, which is decisiveness. We show that this concept can naturally be represented in the context of hypergraph theory, and that decisiveness…

In recent years, reinforcement learning has seen interest because of deep Q-Learning, where the model is a convolutional neural network. Deep Q-Learning has shown promising results in games such as Atari and AlphaGo. Instead of learning the…

We introduce a new type of programming challenge called programming puzzles, as an objective and comprehensive evaluation of program synthesis, and release an open-source dataset of Python Programming Puzzles (P3). Each puzzle is defined by…

This paper presents a novel class of information-theoretic strategies for solving the game of Mastermind, achieving state-of-the-art performance among known heuristic methods. The core contribution is the application of a weighted entropy…

We consider the one-person game of peg solitaire played on a computer. Two popular board shapes are the 33-hole cross-shaped board, and the 15-hole triangle board---we use them as examples throughout. The basic game begins from a full board…

An instance of Max CSP is a finite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satisfied constraints. Max CSP captures many well-known problems (such as Max…