相关论文: Generalizing OOOOOOB
Tiling planar regions with dominoes is a classical problem in which the decision and counting problems are polynomial. We prove a variety of hardness results (both NP- and #P-completeness) for different generalizations of dominoes in three…
We propose a class of two person perfect information games based on weighted graphs. One of these games can be described in terms of a round pizza which is cut radially into pieces of varying size. The two players alternately take pieces…
We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…
We propose and analyse a 2-parameter family of 2-player games on two heaps of tokens, and present a strategy based on a class of sequences. The strategy looks easy, but is actually hard. A class of exotic numeration systems is then used,…
In this work, we examine a generic class of simple distributed balls-into-bins algorithms. Exploiting the strong concentration bounds that apply to balls-into-bins games, we provide an iterative method to compute accurate estimates of the…
Methods of solving big Boolean equations can be broadly classified as algebraic, tabular, numerical and map methods. The most prominent among these classes are the algebraic and map methods. This paper surveys and compares these two types…
The Plurality problem - introduced by Aigner \cite{A2004} - has many variants. In this article we deal with the following version: suppose we are given $n$ balls, each of them colored by one of three colors. A \textit{plurality ball} is one…
Game of Life is a simple and elegant model to study dynamical system over networks. The model consists of a graph where every vertex has one of two types, namely, dead or alive. A configuration is a mapping of the vertices to the types. An…
Many real-world problems modeled by stochastic games have huge state and/or action spaces, leading to the well-known curse of dimensionality. The complexity of the analysis of large-scale systems is dramatically reduced by exploiting mean…
Two-player games on graphs is central in many problems in formal verification and program analysis such as synthesis and verification of open systems. In this work we consider solving recursive game graphs (or pushdown game graphs) that can…
Graph games of infinite length are a natural model for open reactive processes: one player represents the controller, trying to ensure a given specification, and the other represents a hostile environment. The evolution of the system…
Parity games have been broadly studied in recent years for their applications to controller synthesis and verification. In practice, partial solvers for parity games that execute in polynomial time, while incomplete, can solve most games in…
We study impartial take away games on 2 unordered piles of finite nonnegative numbers of tokens $(x,y)$. Two players alternate in removing at least one and at most all tokens from the respective piles, according to certain rules, and the…
We study two forms of a symmetric cooperative game played by three players, one classical and other quantum. In its classical form making a coalition gives advantage to players and they are motivated to do so. However in its quantum form…
Fibonacci nim is a popular impartial combinatorial game, usually played with a single pile of stones. The game is appealing due to its surprising connections with the Fibonacci numbers and the Zeckendorf representation. In this article, we…
Given a finite connected graph $G$, place a bin at each vertex. Two bins are called a pair if they share an edge of $G$. At discrete times, a ball is added to each pair of bins. In a pair of bins, one of the bins gets the ball with…
In the paper it is proven that the two-players turn-based stochastic game "Risk or Safety" has a unique solution. Both players need to play the same strategy if they want to maximize their winning chances. An analytical method based on the…
We consider the one-person game of peg solitaire on a triangular board of arbitrary size. The basic game begins from a full board with one peg missing and finishes with one peg at a specified board location. We develop necessary and…
Generalizing a problem posed by Cover, we propose an adversarial game in which a permutation is incrementally constructed in a setting of partial information. As in the secretary problem, this permutation is exposed in stages via the…
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…