Related papers: High-Precision Estimation of the State-Space Compl…

To investigate the feasibility of strongly solving Minishogi (Gogo Shogi), it is necessary to know the number of its reachable positions from the initial position. However, there currently remains a significant gap between the lower and…

This article describes how to calculate exact space-state complexities of Korean chess and Chinese chess. The state-space complexity (a.k.a. search-space complexity) of a game is defined as the number of legal game positions reachable from…

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…

Shogi is a traditional Japanese strategy board game in the same family as chess, chaturanga, and xiangqi, and has been theoretically studied from various aspects. The research on recommended sequences of moves in each opening of shogi is…

A Sudoku puzzle often has a regular pattern in the arrangement of initial digits and it is typically made solvable with known solving techniques, called strategies. In this paper, we consider the problem of generating such Sudoku instances.…

In this paper, we present a method for finding approximate Nash equilibria in a broad class of reachability games. These games are often used to formulate both collision avoidance and goal satisfaction. Our method is computationally…

We analyse the computational complexity of finding Nash equilibria in simple stochastic multiplayer games. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In…

This paper addresses Monte Carlo algorithms for calculating the Shapley-Shubik power index in weighted majority games. First, we analyze a naive Monte Carlo algorithm and discuss the required number of samples. We then propose an efficient…

Many poker systems, whether created with heuristics or machine learning, rely on the probability of winning as a key input. However calculating the precise probability using combinatorics is an intractable problem, so instead we approximate…

Many puzzle video games, like Sokoban, involve moving some agent in a maze. The reachable locations are usually apparent for a human player, and the difficulty of the game is mainly related to performing actions on objects, such as pushing…

We analyse the computational complexity of finding Nash equilibria in turn-based stochastic multiplayer games with omega-regular objectives. We show that restricting the search space to equilibria whose payoffs fall into a certain interval…

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…

Hashiwokakero, or simply Hashi, is a Japanese single-player puzzle played on a rectangular grid with no standard size. Some cells of the grid contain a circle, called island, with a number inside it ranging from one to eight. The remaining…

We present an analysis of multilevel Monte Carlo techniques for the forward problem of uncertainty quantification for the radiative transport equation, when the coefficients ({\em cross-sections}) are heterogenous random fields. To do this,…

Strength estimation and adjustment are crucial in designing human-AI interactions, particularly in games where AI surpasses human players. This paper introduces a novel strength system, including a strength estimator (SE) and an SE-based…

Correlated equilibria are a fundamental solution concept in game theory. However, despite decades of research, the complexity beyond games of polynomial type -- such as extensive-form games, congestion or routing games, and more broadly…

With the recent surge of interest in using robotics and automation for civil purposes, providing safety and performance guarantees has become extremely important. In the past, differential games have been successfully used for the analysis…

We present the benchmark of the polynomial expansion Monte Carlo method to a Kondo lattice model with classical localized spins on a geometrically frustrated lattice. The method enables to reduce the calculation amount by using the…

This paper introduces Monte Carlo *-Minimax Search (MCMS), a Monte Carlo search algorithm for turned-based, stochastic, two-player, zero-sum games of perfect information. The algorithm is designed for the class of of densely stochastic…