相关论文: Space-state complexity of Korean chess and Chinese…

This paper provides a complexity analysis for the game of dark Chinese chess (a.k.a. "JieQi"), a variation of Chinese chess. Dark Chinese chess combines some of the most complicated aspects of board and card games, such as long-term…

Determining the state-space complexity of the game of Shogi (Japanese Chess) has been a challenging problem, with previous combinatorial estimates leaving a gap of five orders of magnitude ($10^{64}$ to $10^{69}$). This large gap arises…

We analyze the structure of the state space of chess by means of transition path sampling Monte Carlo simulation. Based on the typical number of moves required to transpose a given configuration of chess pieces into another, we conclude…

Automatic chess problem or puzzle composition typically involves generating and testing various different positions, sometimes using particular piece sets. Once a position has been generated, it is then usually tested for positional…

In this paper, we present a board game: Square War. The game definition of Square War is similar to the classic Chinese board game Go. Then we propose a mathematical problem of the game Square War. Finally, we show that the problem can be…

We prove that king chasing problem in Chinese Chess is NP-hard when generalized to $n\times n$ boards. `King chasing' is a frequently-used strategy in Chinese Chess, which means that the player has to continuously check the opponent in…

In this paper we survey the computational time complexity of assorted simple stochastic game problems, and we give an overview of the best known algorithms associated with each problem.

In the field of computational game theory, games are often compared in terms of their size. This can be measured in several ways, including the number of unique game states, the number of decision points, and the total number of legal…

Dou Shou Qi is a Chinese strategy board game for two players. We use a EXPTIME-hardness framework to analyse computational complexity of the game. We construct all gadgets of the hardness framework. In conclusion, we prove that Dou Shou Qi…

Before chess came to Northern Europe there was Tafl, a family of asymmetric strategy board games associated strongly with the Vikings. The purpose of this paper is to study the combinatorial state-space complexity of an Irish variation of…

This paper provides a complexity analysis for the game of reconnaissance blind chess (RBC), a recently-introduced variant of chess where each player does not know the positions of the opponent's pieces a priori but may reveal a subset of…

Unlike repetitions in Western Chess where all repetitions are draws, repetitions in Chinese Chess could result in a win, draw, or loss depending on the kind of repetition being made by both players. One of the biggest hurdles facing Chinese…

We consider finite-state concurrent stochastic games, played by k>=2 players for an infinite number of rounds, where in every round, each player simultaneously and independently of the other players chooses an action, whereafter the…

Kill-all Go is a variant of Go in which Black tries to capture all white stones, while White tries to survive. We consider computational complexity of Kill-all Go with two rulesets, Chinese rules and Japanese rules. We prove that: (i)…

We prove PSPACE-completeness of two classic types of Chess problems when generalized to n-by-n boards. A "retrograde" problem asks whether it is possible for a position to be reached from a natural starting position, i.e., whether the…

The strategic Go game, known for the tedious mathematical complexities, has been used as a theme in many fiction, movies, and books. Here, we introduce the Go game and provide a new version of quantum Go in which the boxes are initially in…

Computational aspects of solution notions such as Nash equilibrium have been extensively studied, including settings where the ultimate goal is to find an equilibrium that possesses some additional properties. Furthermore, in order to…

We review NP-hardness framework and PSPACE-hardness framework for a type of 2D platform games. We introduce a EXPTIME-hardness framework by defining some new gadgets. We use these hardness frameworks to analyse computational complexity of…

Tablut is a complete-knowledge, deterministic, and asymmetric board game, which has not been solved nor properly studied yet. In this work, its rules and characteristics are presented, then a study on its complexity is reported. An upper…

Quantum phenomena have remained largely inaccessible to the general public. This can be attributed to the fact that we do not experience quantum mechanics on a tangible level in our daily lives. Games can provide an environment in which…