Related papers: Mathematical aspect of the combinatorial game "Mah…
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…
Poset games have been the object of mathematical study for over a century, but little has been written on the computational complexity of determining important properties of these games. In this introduction we develop the fundamentals of…
Genetic programming is the practice of evolving formulas using crossover and mutation of genes representing functional operations. Motivated by genetic evolution we develop and solve two combinatorial games, and we demonstrate some…
Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…
Quantum game theory offers a lot of interesting questions, and it is relevant to use the quantum information theory to resolve or improve games with lack of information : how to use the power of quantum entanglement to show the superiority…
We present an algebraic framework for the analysis of combinatorial games. This framework embraces the classical theory of partizan games as well as a number of misere games, comply-constrain games, and card games that have been studied…
In an investigation of the applications of Combinatorial Game Theory to chess, we construct novel mutual Zugzwang positions, explain an otherwise mysterious pawn endgame from "A Guide to Chess Endings" (Euwe and Hooper), show positions…
A combinatorial simplex algorithm is an instance of the simplex method in which the pivoting depends on combinatorial data only. We show that any algorithm of this kind admits a tropical analogue which can be used to solve mean payoff…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
We develop a generic computational model that can be used effectively for establishing the existence of winning strategies for concrete finite combinatorial games. Our modelling is (equational) logic-based involving advanced techniques from…
Mathematics has been used in the exploration and enumeration of juggling patterns. In the case when we catch and throw one ball at a time the number of possible juggling patterns is well-known. When we are allowed to catch and throw any…
There are several approaches for using computers in deriving mathematical proofs. For their illustration, we provide an in-depth study of using computer support for proving one complex combinatorial conjecture -- correctness of a strategy…
We introduce a one-person game that we call Padlock Solitaire which resembles the well-known clock solitaire card game. Analyzing variants of this game we obtain simple proofs of some classical results of combinatorics including ballot…
Cricket is unarguably one of the most popular sports in the world. Predicting the outcome of a cricket match has become a fundamental problem as we are advancing in the field of machine learning. Multiple researchers have tried to predict…
Historically, games of all kinds have often been the subject of study in scientific works of Computer Science, including the field of machine learning. By using machine learning techniques and applying them to a game with defined rules or a…
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…
This paper gives game-theoretic versions of several results on "merging of opinions" obtained in measure-theoretic probability and algorithmic randomness theory. An advantage of the game-theoretic versions over the measure-theoretic results…
Artificial Intelligence (AI) has achieved great success in many domains, and game AI is widely regarded as its beachhead since the dawn of AI. In recent years, studies on game AI have gradually evolved from relatively simple environments…
Kolmogorov complexity is often used as a convenient language for counting and/or probabilistic existence proofs. However, there are some applications where Kolmogorov complexity is used in a more subtle way. We provide one (somehow)…
We investigate some natural probability distributions associated with the game of matroid bingo.