Related papers: Mastermind is NP-Complete
Mastermind is a popular board game released in 1971, where a codemaker chooses a secret pattern of colored pegs, and a codebreaker has to guess it in several trials. After each attempt, the codebreaker gets a response from the codemaker…
Minesweeper is a popular spatial-based decision-making game that works with incomplete information. As an exemplary NP-complete problem, it is a major area of research employing various artificial intelligence paradigms. The present work…
Mastermind is in essence a search problem in which a string of symbols that is kept secret must be found by sequentially playing strings that use the same alphabet, and using the responses that indicate how close are those other strings to…
We study three problems related to the computational complexity of the popular game Minesweeper. The first is consistency: given a set of clues, is there any arrangement of mines that satisfies it? This problem has been known to be…
We show that the Minesweeper game is PP-hard, when the object is to locate all mines with the highest probability. When the probability of locating all mines may be infinitesimal, the Minesweeper game is even PSPACE-complete. In our…
Minesweeper is an interesting single player game based on logic, memory and guessing. Solving Minesweeper has been shown to be an NP-hard task. Deterministic solvers are the best known approach for solving Minesweeper. This project proposes…
Zen Puzzle Garden (ZPG) is a one-player puzzle game. In this paper, we prove that deciding the solvability of ZPG is NP-complete.
In this paper, we study the algorithmic complexity of the Mastermind game, where results are single-color black pegs. This differs from the usual dual-color version of the game, but better corresponds to applications in genetics. We show…
Minesweeper as a puzzle video game and is proved that it is an NPC problem. We use CSP, Logic Inference and Sampling to make a minesweeper solver and we limit us each select in 5 seconds.
From the 1970s up to now, Mastermind, a classic two-player game, has attracted plenty of attention, not only from the public as a popular game, but also from the academic community as a scientific issue. Mastermind with n positions and k…
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…
Many of the famous single-player games, commonly called puzzles, can be shown to be NP-Complete. Indeed, this class of complexity contains hundreds of puzzles, since people particularly appreciate completing an intractable puzzle, such as…
We establish that the subgame perfect equilibrium (SPE) threshold problem for mean-payoff games is NP-complete. While the SPE threshold problem was recently shown to be decidable (in doubly exponential time) and NP-hard, its exact worst…
We study the satisfiability problem for a modal logic expressing knowing-how assertions, which captures an agent's ability to achieve a given goal under the standard semantics based on linear plans. Our main result shows that satisfiability…
We investigate the complexity of a puzzle that turns out to be NL-complete.
Mastermind game is a two players zero sum game of imperfect information. The first player, called codemaker, chooses a secret code and the second player, called codebreaker, tries to break the secret code by making as few guesses as…
We study the average-case complexity of the classic Minesweeper game in which players deduce the locations of mines on a two-dimensional lattice. Playing Minesweeper is known to be co-NP-complete. We show empirically that Minesweeper…
NP complete problem is one of the most challenging issues. The question of whether all problems in NP are also in P is generally considered one of the most important open questions in mathematics and theoretical computer science as it has…
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…
Holzer and Holzer (Discrete Applied Mathematics 144(3):345--358, 2004) proved that the Tantrix(TM) rotation puzzle problem is NP-complete. They also showed that for infinite rotation puzzles, this problem becomes undecidable. We study the…